3 Barium and europium abundances for the stars

We use the same method as in Paper I to derive Ba and Eu abundances for the stars. The synthetic line profiles are computed using the departure coefficients of the Ba II and Eu II levels from the code NONLTE3 (Sakhibullin 1983) and the LTE assumption for other atoms. The line list is extracted from Kurucz' (1994) compilation, and it includes all the relevant atomic and molecular lines. A differential analysis with respect to the Sun is performed. Solar barium and europium abundances, $\log\varepsilon_{\rm Ba,\odot} = 2.21$ and $\log\varepsilon_{\rm Eu,\odot} = 0.53$, and van der Waals damping constants C₆ for the Ba II and Eu II lines were determined in Paper I from solar line profile fitting. The methods of NLTE calculations for Ba II and Eu II were developed earlier (Mashonkina & Bikmaev 1996; Mashonkina et al. 1999; Mashonkina 2000; Paper I). Some examples of the Ba II and Eu II stellar line profile fitting were given in Paper I. Barium abundances have now been determined for the 63 stars most of which are listed in Table 1; for 62 of them abundances are obtained both from the subordinate Ba II lines, $\lambda5853$ and $\lambda6496$, and from the resonance line $\lambda4554$. As discussed earlier the Ba II resonance line is strongly affected by hyperfine structure (HFS) and, as a result, Ba abundances derived from this line depend on the even-to-odd Ba isotope abundance ratio adopted in calculations. A difference between Ba abundances obtained at solar ratio 82:18 (Cameron 1982) and the pure r-process ratio 56:44 (Arlandini et al. 1999) can reach to 0.2 dex (HD45282) and it is minimum (0.08 dex) for the most metal-poor stars of our sample. That is why we prefer to use Ba abundances from the subordinate lines free of HFS effect. However, for the three most metal-poor stars with [Fe/H] < -2 the only subordinate line available, $\lambda6496$, is very weak, and the Ba abundance is determined with an uncertainty of about 0.1 dex. For these stars the resonance line profile leads to a much better fit, and the Ba abundance obtained is more reliable, provided that a realistic even-to-odd Ba isotopic ratio is used. We have shown in Paper I that barium seen in halo stars must have been mainly produced by the r-process. Assuming a pure r-process we have found Ba abundances from the $\lambda4554$ line and compared them with the abundances from the $\lambda6496$ line:

	[Ba $(\lambda4554)_{r}$/Fe]	[Ba $(\lambda6496)$/Fe]
HD84937	-0.02	0.00
BD $2^\circ3375$	-0.11	-0.18
BD $66^\circ268$	0.01	0.07.

For each star the difference $\log\varepsilon_{\rm }(\lambda4554)_r - \log\varepsilon_{\rm }(\lambda6496)$ is within the Ba abundance errors, and keeping in mind that the abundance from the resonance line is more reliable we adopt it as the final Ba abundance. Thus, for these three stars and for BD $34^\circ2476$, with only the resonance line available, Ba abundances have been obtained from the resonance line under the assumption of a pure r-process even-to-odd Ba isotope ratio. For the remaining 59 stars we have obtained Ba abundances from the subordinate lines. If both of them were available the average value was calculated.

Figure 1: The runs of [Ba/Fe] and [Ba/H] with [Fe/H]. Symbols correspond to the thin disk (open circles), the thick disk (filled circles), and the halo stars (asterisks). The two stars indicated by a cross in an open circle are transition stars according to Fuhrmann (1998). Error bars are indicated at the lower left.

Figure 2: Variation of [Eu/Fe] (top panel) and [Eu/H] (bottom panel) with [Fe/H]. Symbols are the same as in Fig. 1.

NLTE effects for Ba II in cool stars were described in detail earlier (Mashonkina et al. 1999). Here we just note that the kinetic equilibrium of Ba II is strongly affected by radiative processes in b-b transitions because this is the dominant ionization stage. As a consequence NLTE effects for Ba II depend on the Ba abundance which correlates with the general metallicity of the model atmosphere. Thus, NLTE leads to a strengthening of the Ba II lines compared with the LTE case at [M/H] > -1.9 and to the opposite effect at lower metallicities. NLTE effects are small for the weakest line  $\lambda5853$. NLTE abundance corrections $\Delta_{\rm NLTE} = \log\varepsilon_{\rm NLTE}-\log\varepsilon_{\rm LTE}$ do not exceed 0.1 dex by absolute value. Significant NLTE effects have been found for the second subordinate line $\lambda6496$: $\Delta_{\rm NLTE}$ is -0.2 dex on average in the metallicity range -1 < [Fe/H] < 0.25; it reduces by absolute value to 0.10-0.15 dex at metallicities between -1.5 and -1, and it becomes positive up to 0.15 dex at even lower [Fe/H]. $\Delta_{\rm NLTE}$ is positive also for the resonance line in the four halo stars with Ba abundances derived from this line. Its value is at maximum for the hottest star, HD84937: $\Delta_{\rm NLTE} = 0.30$ dex and smaller for the coolest star, BD $66^\circ268$: $\Delta_{\rm NLTE}$ = 0.08 dex. For 52 stars with both subordinate lines available the mean value of the difference between NLTE abundances derived from $\lambda6496$ and $\lambda5853$ equals 0.00 $\pm$ 0.03 dex, while under the LTE assumption Ba abundances from the first line are systematically overestimated relative to $\log\varepsilon_{\rm LTE}(\lambda5853)$ with the mean difference of 0.11 $\pm$ 0.04. This gives reason to believe that the uncertainty of our NLTE line formation treatment leads to Ba abundance errors not greater than 0.03 dex.

The final [Ba/Fe] abundance ratios are presented in Table 1 and Fig. 1. In addition, in the bottom panel of Fig. 1 we give [Ba/H]. As the reference solar abundance $\log\varepsilon_{\rm Fe,\odot} = 7.51$ adopted by Fuhrmann (1998,2001) is used in stellar metallicity determinations. As discussed in Paper I, uncertainties of stellar parameters cause abundance errors up to $\Delta \log\varepsilon_{\rm Ba} = 0.11$ dex.

Europium abundances have been derived from the Eu II  $\lambda4129$ line for 51 stars of our sample. Even at spectral resolving power $R = 60\,000$ this line can not be extracted from noise in spectra of the hot halo stars HD19445, HD84937, BD $2^\circ3375$ and BD $34^\circ2476$. For the cool star BD66$^\circ268$, with the lowest metallicity, $\rm [Fe/H] = -2.20$, only a spectrum observed at $R = 40\,000$ is available, and though the Eu II $\lambda4129$ line is detected its profile cannot be satisfactorily fitted. In addition, Eu abundances could not be determined for all the stars observed in May 1997 and September 1996 because no spectra were reduced shortward of 4300 Å.

 

 

Table 2: Mean values $\overline {\rm [Ba/Fe]}$ for thin disk stars of different ages.

Age [Gyr]	Number of stars	$\overline {\rm [Ba/Fe]}$
>8	7	$-0.06 \pm 0.03$
6-8	7	$-0.03 \pm 0.04$
4-6	8	$0.01 \pm 0.07$
2-4	5	$0.06 \pm 0.07$
$\leq$2	3	?

As discussed in Paper I NLTE effects weaken the Eu II  $\lambda4129$ line compared with the LTE case and NLTE abundance corrections are positive. For our stars $\Delta_{\rm NLTE}$ ranges from 0.03 dex to 0.07 dex. The final [Eu/Fe] ratios are presented in Table 1 and Fig. 2, where the run of [Eu/H] with metallicity is shown, too. Uncertainties of stellar parameters cause abundance errors up to $\Delta\log\varepsilon_{\rm Eu} = 0.06$ dex (Paper I). The Eu II  $\lambda4129$ line is located in a crowded spectral range and this can lead to additional errors. To find a continuum level we fitted observed spectra in the spectral range from 4123 Å to 4135 Å. The difference of Eu abundances derived from two spectra of a star is usually within 0.05 dex. We estimate a total Eu abundance error of 0.1 dex.

Figures 1 and 2 confirm the results obtained in Paper I and show new features that have become apparent due to the extension of the stellar sample. We summarize them as follows

• In the halo stars the [Ba/Fe] ratios are mainly between 0.01 and -0.13 with the exception, BD $34^\circ2476$, where barium is evidently overabundant relative to iron: [Ba/Fe] = 0.13. The three halo stars with Eu abundances available show [Eu/Fe] ratios that are close together with a mean value of 0.58;
• The thick disk stars reveal a Ba underabundance relative to iron with a mean value [Ba/Fe] = -0.10 $\pm$ 0.04 (except for BD $0^\circ2245$ with [Ba/Fe] = 0.19; we will return to this star below when discussing other element abundance ratios). A slight decline of the [Ba/Fe] abundance ratios with increasing metallicity should be noted. In contrast to Ba, europium is overabundant relative to iron in thick disk stars with a clear decline of the [Eu/Fe] abundance ratios from about 0.5 at [Fe/H] = -0.9 to 0.25 at [Fe/H] = -0.28;
• The thin disk stars reveal, on average, solar [Ba/Fe] abundance ratios with a mean value of $\overline{\rm [Ba/Fe]} = -0.01 \pm 0.06$ and a decline of the [Eu/Fe] abundance ratios with increasing metallicity. There is a rather large spread in [Ba/Fe] up to 0.3 dex that exceeds Ba abundance errors. At the same time, a spread in [Eu/Fe] is within abundance errors;
• We emphasize that both [Ba/Fe] and [Eu/Fe] abundance ratios reveal a distinction between thick and thin disk stellar populations. This distinction is more evident in the runs of [Ba/H] and [Eu/H] along metallicity (Figs. 1 and 2, bottom panels). In the region of overlapping metallicities Ba abundances in the thick disk stars are lower by 0.1 dex, on average, while Eu abundances are higher by 0.15 dex compared with the thin disk stars.

We note the star HD3795 which reveals a chemical composition closer to the halo than to the thick disk population. From the two high-quality spectra observed at $R\, \simeq 60\,000$ we have determined the elemental abundances:

[Ba/Fe] = 0.02 and 0.01 from the Ba II $\lambda$5853 and $\lambda$6496,

[Eu/Fe] = 0.56 and 0.61 from the Eu II $\lambda$4129 and $\lambda$6645.

The ratios [Ba/Fe], [Eu/Fe] and [Eu/Mg] in this star are higher by 0.12-0.17 dex compared with the corresponding values in other thick disk stars.

Figure 3: The Sr model atom. Linearized transitions are shown as solid lines.

We have tried to find the reason for the large spread of [Ba/Fe] among the thin disk stars and noted a marginal correlation between the [Ba/Fe] abundance ratio and star's age. Stellar ages have been estimated by Bernkopf et al. (2001) using evolutionary tracks of VandenBerg et al. (2000) and recent own calculations. Allowing for an uncertainty of 1 Gyr for the stellar age estimates we combined the stars into separate age groups and calculated for each group the mean value $\overline {\rm [Ba/Fe]}$ (Table 2). We do not give $\overline {\rm [Ba/Fe]}$ for stars younger than 2 Gyr because the three stars available do not represent this group in a statistically reliable way; for two of them, HD43042 and HD130322, $\rm [Ba/Fe] = 0.00$ and 0.03, respectively, and we note a surprisingly low [Ba/Fe] abundance ratio (-0.17) for Procyon (HD61421). It is evident from Table 2 that during thin disk evolution the Ba abundance in interstellar matter increased relative to the iron abundance by about 0.12 dex. So, at least part of the observed spread in [Ba/Fe] may not be random. At the same time, Edvardsson et al. (1993) first noted, and Fuhrmann (2001) confirmed later, that the metallicity of thin disk stars correlates only weakly with the stellar age. For this reason we do not see any regular behaviour of the [Ba/Fe] ratios plotted against [Fe/H] of thin disk stars (Fig. 1).