Free Access
Volume 501, Number 2, July II 2009
Page(s) 519 - 530
Section Galactic structure, stellar clusters, and populations
Published online 29 April 2009

Online Material

Appendix A: Comparison with the 0Z project

The 0Z project (Cohen et al. 2004,2008) has produced a data set similar to that of the ``First Stars'' project, it is therefore of some interest to verify how these data sets compare. Cohen et al. (2004) analysed a set of dwarf stars that is directly comparable to those analysed in the present paper. The spectra were acquired with the HIRES spectrograph at the Keck I Telescope, at a resolution only slightly lower than our UVES-VLT data (34 000 rather than 45 000), and the S/N ratios are comparable. The equivalent widths were measured using an automatic code that fits Gaussians, therefore the general philosphy of EW measurement does not differ from ours. In fact Cohen et al. (2008) observed two giant stars measured by Cayrel et al. (2004), and the equivalent widths compare very well (see Figs. 13 and 14 of Cohen et al. 2008, and related text). The two projects differ in the method used to fix the atmospheric parameters: we use the wings of H$\alpha $ for dwarf stars, while the 0Z project relies on photometry to derive  $T_{\rm eff}$. For surface gravity we use the iron ionisation equilibrium, while the 0Z project relies on theoretical isochrones.

We have also investigated the gf values used by the two projects, and they are very similar, because the use of one or the other set would imply differences in the derived abundances smaller or equal to 0.02 dex. Thus, part of the differences will depend on the different adopted atmospheric parameters. There is no dwarf star in common between the two groups; thus it is not straightforward to compare the results of the two projects.

For the analysis the two projects use different model atmospheres and different line formation codes. We use MARCS model atmospheres and turbospectrum, while the 0Z project uses ATLAS models interpolated in the grid of Kurucz (1993), with the overshooting option switched on, and the MOOG code (Sneden 1973,1974,2007). As we show below, the difference in choice of line formation code is relatively unimportant, implying differences in the abundances of a few hundredths of dex; on the other hand, the choice of ATLAS overshooting models implies abundances that are higher by about 0.1 dex for all the models. Such behaviour has already been noticed by Molaro et al. (1995) for Li, but we show here that it is indeed true for all species.

In Table A.1 we list the abundances for the star HE 0508-1555 derived by using the equivalent widths of Cohen et al. (2004) and their atmospheric parameters ( $T_{\rm eff}$ = 6365, log g = 4.4 and a microturbulent velocity of 1.6  ${\rm km~s^{-1}}$) with three different models: a MARCS model interpolated in our grid, an ATLAS model computed without overshooting, and an ATLAS model computed with overshooting. For all the models we assumed [M/H] = -3.0. Our ATLAS models are somewhat different from those of the Kurucz (1993) used by the 0Z project. In the first place we used the ``NEW'' opacity distribution functions (Castelli & Kurucz 2003) computed with 1  ${\rm km~s^{-1}}$ microturbulence. In the second place we used the Linux version of ATLAS (Sbordone et al. 2004). In all cases the line formation code used was turbospectrum. In the last two columns of Table A.1 we provide the abundances of Cohen et al. (2004), for the reader's convenience.

Inspection of Table A.1 immediately suggests that both the difference in ATLAS versions and the different line formation codes used are immaterial, since the abundances we find for almost all elements are within 0.04 dex of those of Cohen et al. (2004). The two exceptions are Al and Si. For Al there is a good reason for the discrepancy: both Al I lines used are affected by the neighbouring Balmer lines. In our analysis we used spectrum synthesis to derive the abundances. Instead, MOOG can take the absorption due to the Balmer lines into account, either using the opacit switch to introduce a fudge factor on the continuum opacity or using the strong keyword to read strong lines to be considered.

Table A.1:   Abundances for HE 0508-1555 for different model atmospheres.

\end{figure} Figure A.1:

Temperature structure for three models with $T_{\rm eff}$ = 6365, $\log g$ 4.4, and [M/H] = -3.0. The solid line is our MARCS models, the dashed line is an ATLAS overshooting model, the dashed-dotted line is an ATLAS non-overshooting model.

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\end{figure} Figure A.2:

Temperature structure of the deepest layers of three models with $T_{\rm eff}$ = 6365, $\log g$ = 4.4 and [M/H] = -3.0. The solid line is our MARCS models, the dashed-dotted line is an ATLAS non-overshooting model with \ensuremath {\alpha _{{\rm MLT}}} = 1.25 (also shown in Fig. A.1), the dotted line is an ATLAS non-overshooting model with \ensuremath {\alpha _{{\rm MLT}}} = 1.00.

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For Si the difference between our result with the ATLAS overshooting model and the published value of Cohen et al. (2004) is 0.08 dex. This abundance is based on a single line of about 10 pm of EW, therefore clearly saturated. The precise value of the damping constants used for this line and the way the different codes use them may have an impact.

Another inference which can be drawn from Table A.1 is that MARCS models and ATLAS non-overshooting models provide results which are quite similar. This is not the case for the ATLAS overshooting models, which imply abundances which are higher by about 0.1 dex for all elements. The reason for this behaviour may be understood by looking at the temperature structure of the different models. In Fig. A.1 we compare the temperature structures of our MARCS model (solid line), the ATLAS non-overshooting model (dashed-dotted line) and the ATLAS overshooting model (dashed line). The temperature structure of the ATLAS non-overshooting and of the MARCS model are quite similar. In fact, the only difference is for the deepest layers and is driven by the different choices made for the mixing length.

In Fig. A.2 we show the temperature structure of the deeper layers of our MARCS model together with two ATLAS non-overshooting models with different values of \ensuremath {\alpha _{{\rm MLT}}} 1.25 and 1.00. The ATLAS model with \ensuremath {\alpha _{{\rm MLT}}} = 1.00 is closer to the MARCS model, up to $\log\tau_{500}\sim 0.7$, but then becomes hotter than the MARCS model. In general it is impossible to chose \ensuremath {\alpha _{{\rm MLT}}} such that a MARCS and an ATLAS model have exactly the same structure in depth, due to the different formulations of the mixing-length therory in the two codes. Such differences in the very deepest layers have very little influence on a typical abundance analysis. In fact, only the lines that form in these very deep layers are affected, i.e. very weak lines of 0.1 pm or smaller, and the wings of H$\beta$ and higher members of the Balmer series.

In general we can conclude that MARCS and ATLAS non-overshooting models are very similar, and an abundance analysis based on the two models will yield abundances that are consistent within a few hundredths of dex. The situation is dramatically different when we consider the ATLAS overshooting models. Such models present a temperature structure that is very different from both ATLAS non-overshooting and MARCS models in the region $-1 \le \log\tau_{500} \le 1$ where the majority of lines used in abundance analysis are formed.

Castelli et al. (1997a,1997b) extensively investigated the effects of the approximate overshooting present in ATLAS and concluded that the no-overshooting models are capable of reproducing a larger set of observables, thus discouraging the use of overshooting models. To these considerations we may add that, having investigated the mean temperature structures of \ensuremath{{\rm CO}^5{\rm BOLD}} 3D hydrodynamical models, we never saw the typical ``bump'' in the temperature structure seen in ATLAS overshooting models. The real effect of the overshooting is the over-cooling of the outer layers with respect to what is predicted in radiative equilibrium models (Asplund et al. 1999; Collet et al. 2007; Caffau & Ludwig 2007; González Hernández et al. 2008, Paper XI). This is a further reason to avoid the use of the ATLAS overshooting models.

It can be appreciated that the differences due to different models largely cancel out when considering abundance ratios, such as [Mg/Fe], rather than abundances relative to hydrogen. For example, [Mg/H] is -2.04 for the ATLAS non-overshooting model, but -1.90 for the ATLAS overshooting one; however, [Mg/Fe] is 0.50 in the first case and 0.51 in the second case.

A difference in the average [Mg/Fe] is found between us and the 0Z project, of the order of 0.2 dex (the 0Z project being higher), both if we consider only dwarf stars, only giants, or the full samples. Such an offset is roughly compatible with a $1\sigma$ error on each side, but perhaps a little disturbing. Only a 0.01 dex difference is due to the different adopted solar abundances. The use of different models and different atmospheric parameters should largely cancel out when considering a ratio such as [Mg/Fe]. Largely does not mean totally, however: Table C.1 shows a 0.06 dex difference in [Mg/Fe] for BS 16467-062, depending on the adopted atmospheric parameters.

Table 10 of Cohen et al. (2004) is also illuminating by showing how the average [Mg/Fe] changes if one considers the mean computed from the abundances derived from a single line of Mg I. Of the five Mg I lines used by Cohen et al. (2004), three tend to give systematically higher abundances, while two give systematically lower abundances. The final result depends on the set of adopted lines. This issue requires further investigation in the light of the study of deviations from thermodynamic equilibrium for the Mg I lines. Our abundance ratios agree with those provided by the 0Z project, within the stated errors.

At the end of this exercise we concluded that our measurements and those of the 0Z Team are highly consistent. Differences in the published abundances can be traced back to the different atmospheric parameters adopted, the different treatments of convection in the adopted model atmospheres (approximate overshooting versus no overshooting), and for some elements to the particular choice of lines.

Appendix B: Details of the comparison with Lai et al. (2008)

Lai et al. (2008) also analysed a set of stars that is comparable to that of the First Stars project with respect to metallicity. Their sample is also extracted from the HK survey and comprises both dwarfs and giants. Their method of determinng atmospheric parameters is similar to that of the 0Z project, photometric temperatures from the V-K colour and gravities derived from isochrones. They observe the giant star BS 16467-062, also observed by us (Paper V) and in the 0Z project (Cohen et al. 2008) and, not surprisingly, derive atmospheric parameters very close to those of Cohen et al. This allows a very tight comparison of the analysis by the three groups, which we defer to Sect. C.

Lai et al. use the same spectrum synthesis code as ours and also use ATLAS 9 non-overshooting models which, as discussed in Sect. A, are very similar to our MARCS models. It is therefore to be expected that the abundance ratios determined by the two groups are quite similar. In Fig. B.1 we compare the [Mg/Fe] ratios of the First Stars project with those of Lai et al. The overall agreement is satisfactory.

In Fig. B.2 we compare the [O/Fe] ratios of the First Stars project (only giants) with those of Lai et al. The figure seems to indicate good agreement; however we believe that this agreement is in fact fortuitous, as our oxygen abundances were based on the 630 nm [OI] line, while those of Lai et al. have been derived from one OH line of the UV $A^2\Sigma - X^2\Pi $ electronic system around 318.5 nm (although the precise line used is not specified). These OH lines are known to provide very high [O/Fe] ratios when analysed with 1D model atmospheres (e.g. Boesgaard et al. 1999; Israelian et al. 2001). Asplund & García Pérez (2001) explained this behaviour as overcooling of the outer layers of the stars, caused by the overshooting of the convective elements and not properly described by 1D model atmospheres. Our own hdyrodynamical computations (González Hernández et al. 2008, Paper XI) confirm this interpretation. In view of this fact it is, at first sight, surprising to find that Lai et al. determine rather low [O/Fe] ratios from the OH lines. Closer inspection of their analysis reveals, however, that this is mainly driven by their adopted gf values for these lines.

In Fig. B.3 we show a portion of the spectrum of CS 31085-024, used by Lai et al., which we downloaded from the Keck Observatory Archive[*] compared with two synthetic spectra computed using an ATLAS 9 model with the atmospheric parameters adopted by Lai et al. and two different OH line lists. In the first case, we adopted the gf values for the OH lines of the (0-0) vibrational band of the $A^2\Sigma - X^2\Pi $ electronic system computed from the lifetimes calculated by Goldman & Gillis (1981), which we used in Paper IX. In the second case, we used the lines computed by Kurucz. This second list is far richer, since it includes lines from other vibrational bands and not only the (0-0) band. However, even from this limited portion of the spectrum it can be appreciated that the Kurucz gf values are higher than those derived from the Goldman & Gillis (1981) lifetimes; use of the latter gf values would lead to considerably larger OH abundances.

\end{figure} Figure B.1:

Comparison of the [Mg/Fe] ratios of the First Stars project and those of Lai et al. (2008). Our data are shown as circles, while those of Lai et al. as triangles. Open symbols correspond to giant stars, while filled symbols indicate dwarfs.

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\end{figure} Figure B.2:

Comparison of the [O/Fe] ratios of the First Stars project and those of Lai et al. (2008). Symbols as in Fig. B.1. Our oxygen abundances are derived from the 630 nm [OI] line, while those of Lai et al. from one UV OH line of the $A^2\Sigma - X^2\Pi $ electronic system around 318.5 nm.

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\end{figure} Figure B.3:

HIRES-Keck spectrum of the dwarf star CS 31085-024. The data is the same used by Lai et al. (2008), downloaded from the Keck Observatory Archive ( Overlain on the spectrum are two synthetic spectra, computed with SYNTHE, from an ATLAS 9 model with $T_{\rm eff}$ = 5949, $\log g$ = 4.57 and metallicity -3.0 and [O/Fe] = 1.54. The synthetic spectrum plotted in red has been computed using the gf values for the OH lines of the (0-0) vibrational band of the $A^2\Sigma - X^2\Pi $ electronic system computed from the lifetimes calculated by Goldman & Gillis (1981). Instead the one in green has been computed using the line list of the OH  $A^2\Sigma - X^2\Pi $ computed by Kurucz and distributed through (

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For this reason we believe that the oxygen abundances in the stars of the Lai et al. sample should be reinvestigated using a different set of gf values and hydrodynamical model atmospheres. It is likely that the 3D corrections for the giant stars (the majority of the Lai et al. sample with oxygen measurements) are smaller than those for dwarf stars (see Paper XI), since the overcooling is far less extreme in giants than in dwarfs. It is however unlikely that the effect is negligible.

We disagree with the statement by Lai et al., who discard the use of 3D models for the analysis of the OH lines since ``these models seem to overpredict the solar oxygen abundance derived from helioseismology (Delahaye & Pinsonneault 2006)''. In the first place the oxygen abundance in the Sun is not derived from OH UV lines; in the second place, it is now clear that the low solar oxygen abundances that have been claimed in the past (Asplund et al. 2004) are not due to the use of 3D hydrodynamical models, but to low measured EWs and extreme assumptions on the role of collisions with H atoms in the NLTE computations (see Caffau et al. 2008, for a discussion and a new measurement of the solar oxygen abundance). In our view the use of 3D hydrodynamical models is necessary for a reliable analysis of OH lines in metal-poor stars.

The [Cr/Fe] ratios were compared in Fig. 7 and we see that the picture that emerges is very consistent between the two analyses, including the dwarf-giant discrepancy discussed in Sect. 8.1. In agreement with us, Lai et al. note that, when Cr II lines are measurable, the [Cr II/Fe] ratio remains close to zero, suggesting that the decrease in [Cr/Fe] with decreasing metallicity, seen when Cr I lines are used, is probably an artifact due to deviations from LTE.

\end{figure} Figure B.4:

Comparison of the [Zn/Fe] ratios of the First Stars project and those of Lai et al. (2008). Symbols as in Fig. B.1.

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Finally in Fig. B.4 we compare the [Zn/Fe] ratios with those of Lai et al. (2008). They measured Zn in only two dwarfs, slightly more metal-rich than ours and the Zn abundances for these two are in line with what was derived from the giants. We note that the gf value adopted by Lai et al. is 0.04 dex lower than adopted by us.

  Appendix C: Comparison for BS 16467-062

The giant star BS 16467-062 was observed independently by all three groups, ourselves (Cayrel et al. 2004, Paper V), the 0Z project (Cohen et al. 2008), and Lai et al. (2008). The last two groups used HIRES@Keck, while we used UVES@VLT.

In their Appendix B, Cohen et al. (2008) make a detailed comparison between the analysis of giant stars analysed by us and their own analysis. They conclude that the same star analysed by the two groups will show a difference of 0.3 dex in [Fe/H]. This is based on their analysis of the giant star BS 16467-062. We wish to explain how this difference arises. We used the EWs of Cohen et al. (2008) for this star and their gf values to redetermine the abundances using four models: a MARCS model and two ATLAS models (overshooting and non-overshooting) for $T_{\rm eff}$ = 5365 K $\log g$ = 2.95, which are the parameters of Cohen et al. (2008) and the MARCS model with $T_{\rm eff}$ = 5200 K, $\log g$ = 2.50, which was used in Cayrel et al. (2004, Paper V). The results are shown in Table C.1. We omit the results from the ATLAS non-overshooting model, since they are identical to those obtained from the MARCS model. This could be expected by looking at Fig. C.1 in which the temperature structures of the two models are compared.

The differences in the abundances between the MARCS model with the parameters of Paper V and those from an ATLAS overshooting model with the higher $T_{\rm eff}$ and $\log g$ of Cohen et al. (2008) may indeed be as large as 0.3 dex. However, it is important to understand that this difference stems from two distinct factors: on the one hand, the change in $T_{\rm eff}$ and $\log g$, as each species displays a slightly different sensitivity to these; on the other hand, the use of approximate overshooting in the models of Cohen et al. (2008). The two effects are comparable.

Table C.1:   Abundances for BS 16467-062 different model atmospheres and the EWs of Cohen et al. (2008).

\end{figure} Figure C.1:

Temperature structure for three models with $T_{\rm eff}$ = 5365, $\log g$ 2.95 for BS 16467-062. The solid line is our MARCS models, the dashed line is an ATLAS overshooting model, the dashed-dotted line is an ATLAS non-overshooting model.

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The difference in the abundances obtained from the two different MARCS models allow an estimate of the sensitivity of the various abundances to the model parameters. The difference between the MARCS and ATLAS overshooting model allow to see the effect of the approximate overshooting. We confirm that [Fe/H] for this star is 0.3 dex higher using the parameters of Cohen et al. (2008) and an ATLAS overshooting model, relative to what is derived using the parameters of Paper V and a MARCS model (or an ATLAS non-overshooting model). However, 0.17 dex of this difference arises from the different choices in  $T_{\rm eff}$ and $\log g$, and 0.13 dex comes about from the use of the approximate overshooting.

Having understood these differences, we may conclude that there is excellent agreement between the two analyses. With our MARCS model and atmospheric parameters, but the EWs and gf values of Cohen et al. (2008), [Fe/H] for this star is -3.80, which compares very well with -3.77 given in Paper V. Note also that, when using MARCS models (or ATLAS non-overshooting models), our atmospheric parameters achieve a slightly better iron ionisation equilibrium (0.03 dex) than the parameters chosen by Cohen et al. (2008, 0.06 dex). However, since both these differences are much smaller than the line-to-line scatter, it is impossible to chose which set of parameters is better by just looking at the iron ionisation equilibrium. As noted above, most of these differences tend to cancel out when considering abundance ratios.

Iron is the element for which the largest number of lines is measured and, in this respect, its abundance is more robust. For other elements the difference between the values published in Paper V and an analysis by the 0Z Team may also reflect the different choice of lines. For instance for BS 16467-062, Cohen et al. (2008) measure 4 Mg I lines, while in Paper V we measured 8 lines, but used only 7 to derive the mean Mg abundance. The Mg lines in BS 16467-062 are all weak; thus, the re-measurement of the Mg abundance using line profile fitting (see Sect. 6.1) confirms the abundances provided in Paper V.

Table C.2:   Abundances for BS 16467-062 for different atmospheric parameters and the EWs of Lai et al. (2008).

We discarded Mg I 416.7271 nm because the abundance derived from this line strongly deviates from those derived from the other lines. The line is rather weak (0.75 pm as measured in our data or 0.68 pm as measured by Cohen et al. 2008), but even for these very weak lines, the measurements are highly consistent. Thus the mean Mg abundance from our 7 lines is, as given in Paper V, 3.97, with a rather small scatter of 0.09 dex. On the other hand, the mean Mg abundance from the four lines measured by Cohen et al.(2008), including Mg I 416.7271 nm, and using the atmospheric parameters and model of Paper V, is 4.15 with a rather large scatter of 0.33 dex. The mean Mg abundance for these four lines from our measurements is 4.12 with a scatter of 0.38 dex. Finally if we take the measurements of Cohen et al.(2008) and discard the Mg I 416.7271 nm line, we obtain 3.99 with a scatter of 0.11, highly consistent with our published value in Paper V.

The three groups (First Stars, 0Z project, Lai et al.) have used different atmospheric parameters for this star, and the sensitivity of abundances to these is detailed in all three papers. In order to make a stringent comparison between the results of the three groups it is advisable to derive abundances from each set of EWs and gf values for a same model atmosphere and with the same spectrum synthesis code. We did so in Table C.3 where we used the MARCS model used in Paper V to rederive all the abundances. We compared the atomic species in common, excluding Al, for which both we and Lai et al. have used spectrum synthesis.

Table C.3:   Abundances for BS 16467-062 from Paper V and the same model but EWs from Cohen et al. (2008), Lai et al. (2008).

Inspection of Table C.3 immediately reveals that, with very few exceptions, the abundances of the First Stars project rely on more lines than those of the other teams. This is particularly striking for iron, for which we use 130 Fe II lines compared to 55 of Cohen et al. and 52 of Lai et al. A similar situation is found for Ti, where we use 11 Ti I and 23 Ti II lines while Cohen et al. use 2 and 14, respectively, and Lai et al. 1 and 9. This probably reflects that the First Stars spectra have a larger total wavelength coverage and a more uniformly high S/N ratio across the spectra. This in part stems from UVES, as a two-arm spectrograph, covering roughly a 30% wider spectral range in a single exposure than HIRES, and in part to the large amount of telescope time invested in the First Stars project. Once the Mg I line at 416.7 nm has been removed from the set of Cohen et al., the Mg abundance appears to be in remarkably good agreement, in spite of the much larger number of lines used by the First Stars team.

That the actual choice of lines does make a difference is obvious if we look at the Ca abundances. There is a difference of 0.23 dex in the Ca abundance derived in Paper V and that of Cohen et al. (2008). Of the three lines measured by Cohen et al. (2008), we have only two. The mean Ca abundance for these two lines is 2.81 with a 0.05 dex deviation, the discrepancy is reduced to 0.1 dex, totally consistent with the observational errors. We measured all four Ca lines used by Lai et al. (2008), and the mean of these four lines is close to the abundance given in Table C.3. However, Ca I 443.5 nm appears to be discrepant by 0.39 dex with respect to the mean of the other three lines, which is 2.86, only 0.08 dex higher than the value of Lai et al. and fully consistent with observational errors. It is then clear that, for the species for which a limited number of lines is available, the actual choice of lines can make a difference.

Another noticeable difference is for Si. All three groups have determined the Si abundance from a single Si line; however, the other two teams have used the Si I 390.6 nm line, while we used the 410.3 nm line since the other line is heavily contaminated by CH lines in the spectra of giant stars. On the other hand, the EWs for the 390.6 nm line agree well among the three investigations (9.18 pm for us, 9.34 pm for Cohen et al. 2008; and 9.06 nm for Lai et al. 2008); thus the Si abundance derived from this line agrees well among the three investigations.

It is reassuring that for iron, for which all three groups have measured many lines, the results are fully consistent. The conclusion of these comparisons is that the results of the three teams are consistent, once the different choice of atmospheric parameters and models has been factored out. Some caution must be exercised for the species that are represented by few lines, where the actual choice of lines can make a difference, especially if differential NLTE effects are present.

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