5 Strontium abundances

5.1 Solar Sr8pt12ptII lines

The Sr II resonance line $\lambda$4215 and the subordinate line $\lambda$4161 are used in this study to determine stellar Sr abundances. Both of them are blended. Solar profiles of these lines are fitted to improve atomic parameters of blending lines. Another kind of important atomic data is the efficiency of hydrogen collisions in the Sr II kinetic equilibrium calculations which is represented by a scaling factor $k_{\rm H}$ applied to Steenbock & Holweger's (1984) version of Drawin's (1968, 1969) formula for the computation of H atom collisional rates. As mentioned above, the lines $\lambda$10327 and $\lambda$10914 reveal strong NLTE effects, and they are therefore most suitable to estimate this scaling factor from solar line profile fitting.

We use solar flux observations taken from the Kitt Peak Solar Atlas (Kurucz et al. 1984). Our synthetic flux profiles are convolved with a profile that combines a rotational broadening of 1.8 kms^-1 and broadening by macroturbulence with a radial-tangential profile of $V_{\rm mac}= 2.8$ kms^-1 for the infrared lines, $V_{\rm mac}= 3.2$ kms^-1 for $\lambda$4215 and $V_{\rm mac}= 3.5$ kms^-1 for $\lambda$4161. For the solar Sr abundance we accept the meteoritic value $\log\varepsilon_{\rm Sr} = 2.92$ from Grevesse et al. (1996). A depth-independent microturbulence of 0.8 kms^-1 is adopted. For a calculation of van der Waals damping constants C₆ we have derived a formula based on Anstee & O'Mara's (1995) calculations, where

$$\log C_6 = -42.598 + 15.13 \ \alpha + (1 - 2.5\alpha)\log v \\ + 2.5 \log \Upsilon, \nonumber$$

with

$$\Upsilon = \Bigl( \frac{\sigma_0}{\pi} \ \Gamma \Bigl(\frac{4 - \alpha}{2}\Bigr) \Bigr)\cdot$$

Here $v = (8\,kT/\pi\mu)^{1/2}$ and $\mu = M_{\rm A}M_{\rm H}/(M_{\rm A}+M_{\rm H})$ is the reduced mass; $\sigma_0$ is a line-broadening cross-section and $\alpha$ is a velocity parameter. The values of $\sigma_0$ and $\alpha$ are tabulated in the papers of Anstee & O'Mara (1995), Barklem & O'Mara (1997,2000), and Barklem et al. (1998). The C₆-value depends only slightly on temperature as $T^{0.5 - 1.25 \alpha}$. At typical values of $\alpha$ (between 0.2 and 0.4) $\log C_6$ changes by 0.04 at maximum as one goes from T = 4000 K to T = 6000 K. Therefore the small variation of C₆ across line formation layers can be neglected in calculations of line profiles, and we use in this study depth-independent C₆-values computed at T = 6000 K.

$\vec\lambda$10327 and $\vec\lambda$10914. We use $\log gf$ ($\lambda$10327) = -0.35 and $\log gf$ ($\lambda$10914) = -0.64 according to Wiese & Martin (1980). The recent results of Guet & Johnson (1991) and Brage et al. (1998) give similar values: $\log gf$ ($\lambda$10327)  = -0.30 and -0.34, respectively, and $\log gf$ ($\lambda$10914) = -0.59 and -0.62. The C₆-values for these lines (Table 3) have been computed with $\sigma_0$ and $\alpha$ taken from Barklem & O'Mara (2000).

We compared different atomic models excluding and including H atom collisions with cross-sections calculated according to Steenbock & Holweger (1984) and scaled by various factors $k_{\rm H}$. If hydrogen collisions are neglected we obtain for both lines broader and deeper theoretical profiles compared with the observed ones. Inclusion of these processes with $k_{\rm H}$= 0.1 makes the NLTE profile shallower and narrower than the observed one. The best fits of both lines are obtained at $k_{\rm H}$= 0.01. In Fig. 5 (bottom panel) we show one of these lines, $\lambda$10327. For comparison the LTE profile corresponding to the same fitting parameters is presented, too. It is obvious that assuming LTE we cannot fit the $\lambda$10327 line profile with reasonable values of $\log\varepsilon_{\rm Sr}$ and $V_{\rm mic}$; even the line wings are affected by NLTE effects.

$\vec\lambda$4215. The Sr II resonance lines are affected by hyperfine structure (HFS). Strontium is represented by four stable isotopes. For solar system matter the ratio of the even Sr isotopes to the odd ones ( $^{84}{\rm Sr}$+ $^{86}{\rm Sr}$+ $^{88}{\rm Sr}$): $^{87}{\rm Sr}$ is 93:7 according to Cameron (1982). Isotopic shifts are very small ($\leq$ $2~\rm m\AA$) but the odd isotopes have hyperfine splitting of their levels resulting in several HFS components for a spectral line. We use the data on wavelengths and relative intensities of HFS components given by McWilliam et al. (1995). Oscillator strengths of separate components (Table 3) have been calculated using solar Sr isotopic abundances and $\log gf (\lambda4215) = -0.172$ from Wiese & Martin (1980). The most recent value $\log gf (\lambda4215) = -0.175$ of Brage et al. (1998) coincides with that adopted in our study.

  

Table 3: Atomic data for the Sr II lines. Most of the entries are self-explanatory; f_ij of the HFS components correspond to Sr isotopic abundances of solar system matter.

The Sr II $\lambda$4215.539 Å line is blended by the strong Fe I $\lambda$4215.426 Å line and by a few CN molecular lines in the far blue and red line wings. We treat Fe I $\lambda$4215 with the fixed values of $\log gf = -1.76$ and $\log C_6 = -30.69$. The last value was calculated using the above formula. For the Sun $\log\varepsilon_{\rm Fe}$ = 7.51 was adopted. Oscillator strengths of the CN molecular lines were fitted to reproduce the observed blend profile.

Figure 6: NLTE synthetic (continuous line) and pure Sr II line profiles (dotted) compared with observed FOCES spectra (bold dots) of HD69611 ([Fe/H] = -0.60, top row), HD144579 ([Fe/H] = -0.69, bottom row, left panel) and HD84937 ([Fe/H] = -2.07, bottom row, right panel).

Sr II $\lambda$4215 is strongly affected by van der Waals damping. The classical Unsöld (1955) formula gives $\log C_6 = -32.275$ while the formula above leads to $\log C_6 = -31.805$ with $\sigma_0$ and $\alpha$ from Barklem & O'Mara (2000). Varying $\log C_6$ by only 0.1 has a significant effect on the total energy absorbed in this line. A careful analysis of the solar line profile makes possible a separation of collisional broadening and blending effects. The best fit obtained with $\log C_6 = -32.02$ is presented in Fig. 5 (top panel). For comparison we give also the pure Sr II $\lambda$4215 NLTE profile calculated with the same parameters.

We did not succeed fitting the $\lambda$4215 line core (Fig. 5) because it is formed in the uppermost atmospheric layers above $\log\tau_{5000} = -4$, and it is most probably influenced by a non-thermal and depth-dependent chromospheric velocity field that is not part of our solar model.

$\vec\lambda$4161. This line is located in the far red wing of two strong blends, Fe I $\lambda$4161.488 Å and Ti II $\lambda$4161.534 Å. In addition, absorption in a few CN and SiH molecular lines near 4161.8 Å lowers the continuum flux by about 5%. We have found that $\log gf = -0.50$ given by Wiese & Martin (1980) does not allow to reproduce the solar Sr II $\lambda$4161 line with a fixed value of $\log\varepsilon_{\rm Sr}$ = 2.92 and reasonable values of $V_{\rm mic}$. The best fit (Fig. 5, middle panel) is obtained with $\log gf = -0.41$ and $\log C_6 = -31.4$. The last value is larger by 0.1 compared with the classical Unsöld (1955) constant.

5.2 Stellar Sr abundances

As mentioned above both Sr II lines of interest are blended. To obtain a good line profile fitting of the stellar spectra and, thus, to reduce Sr abundances errors we use only the spectra observed at $R \simeq 60\,000$ in 1998 to 2000. An exception refers to the four stars, HD45282, HD194598, HD201891 and BD$66^\circ$268, particularly important for our study. In total, Sr abundances have been determined for 49 stars and for 36 of them from both Sr II lines. The weaker $\lambda$4161 line disappears at [Fe/H] < -1. As an example, we give in Fig. 6 the Sr II $\lambda$4215 line profiles for the three metal-poor stars and the Sr II $\lambda$4161 line profile for one of them. The contribution of the Fe I $\lambda$4215.426 Å line blend reduces rapidly with decreasing [Fe/H] because the electron number density affects line strengths of minor species such as Fe I much more than those of dominant ionization stages such as Sr II. It can be seen in Fig. 6 (right column, bottom panel) that for HD84937 the contribution of the Fe I $\lambda$4215 line is negligible. This holds also for the other 3 stars of our sample with [Fe/H] < -1.9 and $T_{\rm eff}>$ 6000 K.

NLTE effects for the Sr II lines are small for all the stars of our sample: NLTE abundance corrections $\Delta_{\rm NLTE}$ are negative for $\lambda$4215 and positive for $\lambda$4161 and do not exceed 0.07 dex and 0.05 dex, respectively, by absolute value. For 36 stars with both Sr II lines investigated a difference of NLTE abundances derived from $\lambda$4215 and $\lambda$4161 is mainly within 0.08 dex with the mean value of 0.00 $\pm$ 0.06 dex while the mean difference of LTE abundances is 0.05 $\pm$ 0.06 dex.

Figure 7: The run of [Sr/Fe] with [Fe/H]. Symbols are the same as in Fig. 1.

In general, Sr abundances derived from the resonance line depend on the even-to-odd Sr isotope ratio adopted in calculations. We concluded in Paper I that Ba and Eu in halo and thick disk stars were mainly produced by r-process in high-mass stars. Sr might be produced not only in the r-process but also in a weak s-process that is related to high mass stars, too. According to Arlandini et al. (1999) the r-process contributes only to the $^{88}{\rm Sr}$ isotope; the consequence of a dominating r-process is therefore the disappearance of HFS components in the Sr II lines. On the other hand the separation of HFS components of the $\lambda$4215 line is not large (35 mÅ at maximum, see Table 3); Sr abundances derived from $\lambda$4215 with and without HFS thus differ by 0.07 dex at [Fe/H] $\simeq -2$. According to Beer et al. (1992) the weak s-process produces much more even Sr isotopes than odd ones: ( $^{86}{\rm Sr}$ + $^{88}{\rm Sr}$): $^{87}{\rm Sr}$ = 93:7, similarly to the main s-process which defines the solar system even-to-odd Sr isotope ratio. The ratio of the weak s- to r-process is estimated as 3:2 (Arlandini et al. 1999). Consequently, the use of a solar even-to-odd Sr isotope ratio leads to an uncertainty of Sr abundances in halo and thick disk stars of not more than 0.02-0.03 dex. We neglect such a small value and use the solar even-to-odd Sr isotope ratio for all stars of our sample.

The final [Sr/Fe] are presented in Table 1 and Fig. 7. Whenever both Sr II lines were available the average value was calculated. It can be concluded from Fig. 7 that the general behaviour of the [Sr/Fe] abundance ratios with respect to metallicity is similar to that of [Ba/Fe] (Fig. 1, top panel). For the thin disk stars there is a spread in [Sr/Fe] up to 0.3. Similarly to [Ba/Fe] this points to a correlation of [Sr/Fe] with stellar age: for 12 stars older than 5 Gyr the mean value $\overline{\rm [Sr/Fe]} = -0.10$ while for 7 stars younger than 5 Gyr $\overline{\rm [Sr/Fe]} = 0.04$. The thick disk stars show a decline of [Sr/Fe] with [Fe/H] increasing, so, that in "late'' thick disk stars ([Fe/H] > -0.5) strontium is underabundant relative to iron by 0.1 dex, and this value coincides with the Ba underabundance reported in Sect. 3 for the thick disk stars. Underabundances of Sr relative to iron are typical for the halo stars which are close together with a mean value of [Sr/Fe] = -0.10 $\pm$ 0.02. The discrepant result for BD$34^\circ$2476 was dropped (see Sect. 6 for further discussion of this star).

The thick disk star, BD$0^\circ$2245 ([Fe/H] = -1.13), reveals a Sr overabundance relative to iron similar to that found for Ba (Sect. 3). There is no HIPPARCOS parallax for this star and the uncertainty of stellar parameters could explain apparent peculiar abundances of Sr and Ba. Another explanation would be that this star was the secondary component of a binary, and that we observe accreted s-process products formed in the evolved primary component.

There are only a few Sr abundance studies of cool stars in the literature. For the sample of 16 stars including dwarfs, giants and supergiants Gratton & Sneden (1994) have found small Sr excess in the metallicity range from -0.9 down to -2.8 with the mean value [Sr/Fe] = 0.07 $\pm$ 0.11 (10 stars) and slight underabundance of Sr relative to Fe up to 0.15 dex for 6 stars with [Fe/H] > -0.6. These data are based on the examination of equivalent widths of the Sr II $\lambda$4161 line, and the authors note that the [Sr/Fe] ratios given by the Sr II resonance line at 4215 Å are smaller by 0.21 $\pm$ 0.04 dex. The mean ratio [Sr/Fe] = -0.14 deduced from $\lambda$4215 line for the halo stars is in agreement with that found in the present study. At [Fe/H] < -1 the Sr II subordinate line is rather weak, and in our opinion Sr abundances based on the Sr II $\lambda$4215 line are more reliable than those derived from Sr II $\lambda$4161. Using equivalent widths of Sr II $\lambda$4077 and $\lambda$4215 for a sample of cool dwarfs in the metallicity range similar to ours, Hartmann & Gehren (1988) have obtained [Sr/Fe] abundance ratios close to solar, independent of the general metal abundance. However, the large scatter of up to 0.5 dex masks any features in the run [Sr/Fe] vs. [Fe/H]. Based on the Sr I $\lambda$4607 line Jehin et al. (1999) have obtained [Sr/Fe] abundance ratios between 0 and -0.4 for a sample of 21 mildly metal-poor stars in the narrow metallicity range from -0.8 down to -1.3. We note that using the LTE assumption may result in an underestimate of element abundances derived from spectral lines of minor species such as Sr I. Magain (1989) has studied only metal-poor stars with [Fe/H] < -1.4 and obtained a Sr excess of about 0.4 dex at [Fe/H] between -1.5 and -2.5 and a decline of the [Sr/Fe] abundance ratios at lower metallicities, however, he notes that results for Sr should be considered as preliminary due to the strength of the available lines (Sr II $\lambda$4077 and $\lambda$4215) and the uncertainties affecting the gf-values as well as the damping constants. In the range of overlapping metallicities his data are different from ours. For extremely metal-poor stars with [Fe/H] < -2.4 McWilliam et al. (1995) and Ryan et al. (1996) have found a decline of the [Sr/Fe] abundance ratios with decreasing metallicity and a spread in these ratios up to 2.5 dex. Elemental abundances were determined from the Sr II $\lambda$4077 and $\lambda$4215 lines with the LTE assumption. It was noted in Sect. 4 that for extremely metal-poor stars NLTE effects for the Sr II lines depend strongly on stellar parameters. We give one example. For two stars of Ryan et al. sample, BS16968-061 ( $T_{\rm eff}$ = 6000 K, $\log g$ = 4, [Fe/H] = -3.08) and CS22186-005 ( $T_{\rm eff}$ = 6000 K, $\log g$ = 2, [Fe/H] = -2.77), we have computed NLTE abundance corrections $\Delta_{\rm NLTE}$ = 0.25 dex and 0.60 dex, respectively. Based on NLTE Sr abundances we obtain for these stars new values [Sr/Fe] = -0.25 and -0.63 instead of -0.50 and -1.23 as determined by Ryan et al. Therefore, the large spread in [Sr/Fe] ratios published by McWilliam et al. (1995) and Ryan et al. (1996) may be at least in part due to neglecting NLTE effects for the Sr II lines.

Figure 8: Variation of element abundance ratios with [Fe/H]. Symbols are the same as in Fig. 1. Dotted lines in the top panel limit the range of the [Eu/Ba]r ratio uncertainty.