$\begin{figure}\resizebox{\hsize}{!}{\includegraphics{ds1800f6.eps}}\end{figure}$

Figure 6: The abundances of $\alpha$ elements, Fe and Ba as a function of logarithmic age. The symbols are shown in Fig. 7

Figure 6 shows the age-metallicity relations for $\alpha$ , iron and barium elements, where $\alpha$ represents the mean abundance of Mg, Si, Ca and Ti. Generally, there is a loose correlation between age and abundance. Stars younger than 5 Gyr ( $\log \tau_{9} < 0.7$ ) are more metal-rich than $\mbox{\rm [Fe/H]}\simeq -0.3$ , and stars with $\mbox{\rm [Fe/H]}< -0.5$ are not younger than 6-7 Gyr ( $\log \tau_{9} > 0.8$ ). The deviating young halo star HD97916 (indicated by an asterisk in Fig. 6) is discussed in Sect. 8.

The correlation between age and abundance is, however, seriously distorted by a considerable scatter. Stars with solar metallicity have an age spread as large as 10 Gyr, and coeval stars at 10 Gyr show metallicity differences as high as 0.8 dex. Such a dispersion cannot be explained by either the abundance error (< 0.1 dex) or the age uncertainty ( $\sim 15$ %) in the AMR. This is an important constraint on GCE models, which must reproduce both the weak correlation and the substantial dispersion.

It is seen from Fig. 6 that Ba has the steepest slope in the AMR, Fe has intermediate slope, and the $\alpha$ elements show only a very weak trend with [Fe/H]. This was also found by EAGLNT and is consistent with nucleosynthesis theory that suggests that the main synthesis sites of Ba, Fe and $\alpha$ elements are AGB stars ( $1-3~M_{\odot}$ ), SNe Ia ( $6-8~M_{\odot}$ ) and SNe II ( $> 8~M_{\odot}$ ), respectively. Due to their longer lifetime, lower mass stars contribute to the enrichment of the Galaxy at a later epoch, i.e. after massive stars have been polluting their products into the ISM. Hence, the Ba abundance is relatively low in the beginning of the disk evolution and increases quickly in the late stage, leading to a steeper slope.

It is interesting that there is a hint of a smaller metallicity spread for young stars with $\log \tau_{9}=0.4-0.8$ in this work than in EAGLNT, while the spread is similar for old stars. If we are not misled by our sample (less young stars than in the EAGLNT sample and a lack of stars with $\log \tau_{9}<0.4$ ), it seems that there are metal-rich stars at any time in the solar neighbourhood while metal-poor stars are always old. Another interesting feature for the young stars is that [Ba/H] has a smaller metallicity spread than [Fe/H] and [ $\alpha$ /H]. This could be due to the dependence of elemental yield on the progenitor's mass. Ba is produced by AGB stars with a rather small mass range of 1-3 $M_{\odot}$ , while Fe and $\alpha$ elements are synthesized by SNe having a mass range $\sim 6-30$ $M_{\odot}$ .

7.1.2 Stellar kinematics as functions of age and metallicity

The study of the dispersion in kinematical parameters as a function of Galactic time is more interesting than the kinematical data alone, because any abrupt increase in dispersion may indicate special Galactic processes occurring during the evolution. Generally, dispersions in $\mbox{$V_{\rm LSR}$ }$ , $\mbox{$W_{\rm LSR}$ }$ and total velocity increase with stellar age. We have not enough stars at $\sim$ 2.5 Gyr and 10 Gyr to confirm the abrupt increases in the $\mbox{$W_{\rm LSR}$ }$ dispersion found by EAGLNT at these ages. Instead, our data seems to indicate that the kinematical dispersion (possibly also the metallicity) is fairly constant for stars younger than 5 Gyr ( $\log \tau_{9}=0.7$ ), but it increases with age for stars with $\log \tau_{9}>0.7$ . Coincidentally, 5 Gyr corresponds to $\mbox{\rm [Fe/H]}\simeq -0.4$ dex, the metallicity where EAGLNT suggested an abundance transition related to a dual formation of the Galactic disk. The abundance transition at $\mbox{\rm [Fe/H]}\simeq -0.4$ dex is confirmed by our data, but the increase of the $\mbox{$W_{\rm LSR}$ }$ dispersion at $\mbox{\rm [Fe/H]}\simeq -0.4$ found by EAGLNT is less obvious in our data.

$\begin{figure}\resizebox{\hsize}{!}{\includegraphics{ds1800f7.eps}}\end{figure}$

Figure 7: $\mbox{$V_{\rm LSR}$ }$ vs. $\mbox{\rm [Fe/H]}$ with different symbols showing three groups of stars. The asterisk indicates the halo star HD97916 discussed in Sect. 8

When the velocity component in the direction of Galactic rotation, $\mbox{$V_{\rm LSR}$ }$ , is investigated as a function of the metallicity (see Fig. 7), we find that there are two subpopulations for $\mbox{\rm [Fe/H]}\leq -0.6$ with positive $\mbox{$V_{\rm LSR}$ }$ in group A and negative $\mbox{$V_{\rm LSR}$ }$ in group C, while stars with $\mbox{\rm [Fe/H]}\geq -0.6$ have $\mbox{$V_{\rm LSR}$ }$ around $\mbox{$V_{\rm LSR}$ }= -10 \mbox{\rm\,km\,s$^{-1}$ }$ (group B). The pattern persists when other elements are substituted for Fe. As shown in Edvardsson et al. ([1993b]), there is a tight correlation between $\mbox{$V_{\rm LSR}$ }$ and the mean Galactocentric distance in the stellar orbit, $R_{\rm m}$ . Hence, we can trace the metallicity at different Galactocentric distances assuming that $R_{\rm m}$ is a reasonable estimator of the radius of the star's original orbit. Note, however, that the lower metallicity toward the Galactic center ( $\mbox{$V_{\rm LSR}$ }\lesssim -50 \mbox{\rm\,km\,s$^{-1}$ }$ ) for group C stars may be due to their large ages. Excluding these stars, a trend of decreasing metallicity with increasing $\mbox{$V_{\rm LSR}$ }$ for stars with similar age is found, which indicates a radial abundance gradient in the disk, and thus suggests a faster evolution in the inner disk than the outer. This is compatible with a higher SFR, due to the higher density, in the inner disk.

There are two possibilities to explain the stars in group C. One is anchored to the fact that the oldest stars (> 10 Gyr) in our sample have the lowest $\mbox{$V_{\rm LSR}$ }$ , i.e. the smallest $R_{\rm m}$ , indicating that the Galaxy did not extend to the Sun at 10 Gyr ago according to an inside-out formation process of the Galaxy. The other is that these stars come from the thick disk, which is older and more metal-poor than the thin disk.

7.2 Relative abundances

7.2.1 Oxygen and magnesium

In agreement with most works, [O/Fe] shows a tendency to decrease constantly with increasing metallicity for disk stars. As oxygen is only produced in the massive progenitors of SNe II, Ib and Ic, it is mainly build up at early times of the Galaxy, leading to an overabundance of oxygen in halo stars. The [O/Fe] ratio gradually decline in the disk stars when iron is produced by the long-lived SNe Ia. The time delay of SNe Ia relative to SNe II is responsible for the continuous decrease of oxygen in disk stars. The tendency for [O/Fe] to continue to decrease at $\mbox{\rm [Fe/H]}> -0.3$ argues for an increasing ratio of SNe Ia to SNe II also at the later stages of the disk evolution.

In general, the relation of [O/Fe] vs. $\mbox{$V_{\rm LSR}$ }$ reflects the variation of [Fe/H] with $\mbox{$V_{\rm LSR}$ }$ (see Fig. 7). [O/Fe] decreases with increasing $\mbox{$V_{\rm LSR}$ }$ for stars with $\mbox{$V_{\rm LSR}$ }< 0$ and slowly increase with further larger $\mbox{$V_{\rm LSR}$ }$ . Considering their similar ages, the decreasing [O/Fe] from group A to group B stars may be attributed to the increasing $\mbox{$V_{\rm LSR}$ }$ , whereas the higher [O/Fe] of group C is due to an older age.

$\begin{figure}\resizebox{\hsize}{!}{\includegraphics{ds1800f8.eps}}\end{figure}$

Figure 8: Abundance patterns for elements from O to Ba. The symbols are the same as in Fig. 7 and their size is proportional to stellar age. Note that the trends of [Al/Fe] and [K/Fe] may be spurious due to the neglect of non-LTE effects

The magnesium abundance shows a decreasing trend with increasing metallicity like oxygen for $\mbox{\rm [Fe/H]}< -0.3$ but it tends to flatten out for higher metalicities. Given that magnesium is theoretically predicted to be formed only in SNe II, the similar decreasing trend as oxygen is easily understood, but the flat [Mg/Fe] towards higher metallicities than $\mbox{\rm [Fe/H]}> -0.3$ is unexpected. It seems that SNe II are not the only source for Mg. Perhaps SNe Ia also contribute to the enrichment of Mg during disk evolution.

The flat trend of [Mg/Fe] vs. [Fe/H] for $\mbox{\rm [Fe/H]}> -0.3$ is also evident from the data of EAGLNT if the high Mg/Fe ratios of their NaMgAl stars are reduced to a solar ratio as found by Tomkin et al. ([1997]). Feltzing and Gustafsson ([1999]) also find [Mg/Fe] to be independent of metallicity for their more metal-rich stars although the scatter is large.

With more magnesium lines in the present study, we get a similar scatter of [Mg/Fe] as EAGLNT. The scatter is slightly larger than that of oxygen and in particular much larger than those of Si and Ca. Although we do not find a large line-to-line scatter in the Mg abundance determination, it is still unclear if the scatter in [Mg/Fe] is cosmic. Only 3 Mg I lines are available for most stars while Si and Ca are represented by 20-30 lines. There is no obvious evidence showing the scatter to be an effect of different $\mbox{$V_{\rm LSR}$ }$ . Nor do we find a clear separation of thick disk stars from thin disk stars in the diagram of [Mg/Fe] vs. [Mg/H], as has been found by Fuhrmann ([1998]). It seems that neither observation nor theory is satisfactory for Mg.

7.2.2 Silicon, calcium and titanium

Both Si and Ca have a very small star-to-star scatter (0.03 dex) at a given metallicity for thin disk stars. The scatter is slightly larger among the thick disk stars. Since the scatter corresponds to the expected error from the analysis, we conclude that the Galactic scatter for [Si/Fe] and [Ca/Fe] is less than 0.03 dex in the thin disk.

[Ti/Fe] was shown by EAGLNT to be a slowly decreasing function of [Fe/H] and the decrease continues to higher metallicity. Our data show a similar trend but the continuous decrease toward higher metallicity is less obvious with a comparatively large star-to-star scatter. There is no evidence that the scatter is correlated with $\mbox{$V_{\rm LSR}$ }$ . We note that Feltzing & Gustafsson ([1999]) find a similar scatter in [Ti/Fe] for metal-rich stars with the Ti abundance based on 10-12 Ti I lines.

7.2.3 Sodium and aluminum

Na and Al are generally thought to be products of Ne and C burning in massive stars. The synthesis is controlled by the neutron flux which in turn depends on the initial metallicity and primarily on the initial O abundance. Therefore, one expects a rapid increase of [Na/Mg] and [Al/Mg] with metallicity. But our data shows that both Na and Al are poorly correlated with Mg in agreement with EAGLNT. This means that the odd-even effect has been greatly reduced in the nucleosynthesis processes during the disk formation.

When iron is taken as the reference element, we find that [Na/Fe] and [Al/Fe] are close to zero for $\mbox{\rm [Fe/H]}$ < -0.2, while EAGLNT found 0.1-0.2 dex differences between $\mbox{\rm [Fe/H]} = -0.2$ and $\mbox{\rm [Fe/H]}= -1.0$ . Our results support the old data by Wallerstein ([1962]) and Tomkin et al. ([1985]), who suggested [Na/Fe] $\sim$ 0.0 for the whole metallicity range of the disk stars. The situation is the same for Al; EAGLNT found an overabundance of [Al/Fe] $\simeq 0.2$ for $\mbox{\rm [Fe/H]}< -0.5$ , whereas we find a solar ratio for the low metallicity stars. As discussed in Sect. 5.3 this may, however, be due to a non-LTE effect.

In the case of the more metal rich stars the abundance results for Na and Al are rather confusing. EAGLNT found that some metal-rich stars in the solar neighbourhood are rich in Na, Mg and Al, but the existence of such NaMgAl stars was rejected by Tomkin et al. ([1997]). Several further studies, however, confirmed the overabundance of some elements again. Porte de Morte ([1996]) found an overabundance of Mg but not of Na. Feltzing & Gustafsson ([1999]) confirmed the upturn of [Na/Fe] but their metal-rich stars did not show Mg and Al overabundances. In the present work we find a solar ratio of Na/Fe up to $\mbox{\rm [Fe/H]}\simeq 0.1$ , and a rather steep upturn of [Al/Fe] beginning at $\mbox{\rm [Fe/H]}\simeq -0.2$ . As discussed in Sect. 5.3, our Al abundances may, however, be severely affected by non-LTE effects. We conclude that more accurate data on Na and Al abundances are needed.

7.2.4 Potassium

7.2.5 Vanadium, chromium and nickel

Ni follows iron quite well at all metallicities with a star-to-star scatter less than 0.03 dex. Two features may be found after careful inspection. Firstly, there is a hint that [Ni/Fe] slightly decreases with increasing metallicity for $-1.0 < \mbox{\rm [Fe/H]}< -0.2$ . The trend is more clear, due to smaller star-to-star scatter, than in EAGLNT. Secondly, there is a subtle increase of [Ni/Fe] for $\mbox{\rm [Fe/H]}> -0.2$ . Interestingly, Feltzing & Gustafsson ([1999]) found a slight increase of [Ni/Fe] towards even more metal-rich stars.

7.2.6 Barium

Barium is thought to be synthesized by neutron capture s-process in low mass AGB stars with an evolutionary timescale longer than that of iron-producing SNe Ia. Therefore, [Ba/Fe] is still slightly underabundant at $\mbox{\rm [Fe/H]}= -1.0$ . Ba is then enriched significantly at later stages of the disk evolution, but the decrease of [Ba/Fe] for more metal-rich stars beginning with $\mbox{\rm [Fe/H]}\sim -0.2$ is unexpected.

Given that the low [Ba/Fe] for some stars may be related to their ages, the relation of [Ba/Fe] vs. [Fe/H] at different age ranges was investigated (see Fig. 9). In agreement with EAGLNT, the run of [Ba/Fe] vs. [Fe/H] in old stars with $\log \tau_{9} > 0.9$ ( $\sim$ 8 Gyr) and $0.7 <\log \tau_{9} < 0.9$ shows a flat distribution for $\mbox{\rm [Fe/H]}< -0.3$ and a negative slope for $\mbox{\rm [Fe/H]}> -0.3$ . All young stars with $\log \tau_{9} < 0.7$ ( $\sim$ 5 Gyr) have $\mbox{\rm [Fe/H]}> -0.3$ and a clear decreasing trend of [Ba/Fe] with [Fe/H] is seen. In addition, there is a hint of higher [Ba/Fe] for younger stars both in the interval $-0.7 <\mbox{\rm [Fe/H]} <-0.3$ , where [Ba/Fe] is constant, and in the interval $\mbox{\rm [Fe/H]}> -0.3$ , where [Ba/Fe] is decreasing. This is consistent with the formation of young stars at a later stage of the disk when long-lived AGB stars have enhanced Ba in the ISM. The flat [Ba/Fe] for $\mbox{\rm [Fe/H]}< -0.3$ may be explained by the suggestion of EAGLNT that the synthesis of Ba in AGB stars is independent of metallicity, i.e. that Ba shows a primary behaviour during the evolution of the disk. But the age effect alone cannot explain the underabundant [Ba/Fe] in metal-rich stars, because [Ba/Fe] decreases with metallicity for all ages after $\mbox{\rm [Fe/H]}= -0.3$ . One reason could be that s-element synthesis occurs less frequently in metal-rich AGB stars possibly because the high mass loss finishes their evolution earlier.

$\begin{figure}\resizebox{\hsize}{!}{\includegraphics{ds1800f9.eps}}\end{figure}$

Figure 9: Different relations of [Ba/Fe] vs. [Fe/H] for stars with different age ranges: $\log \tau_{9} < 0.7$ (filled circles), $\log \tau_{9} = 0.7 -0.9$ (crosses) and $\log \tau_{9} > 0.9$ (open circles)

7 Results and discussion

7.1 Relations between abundances, kinematics and ages

7.1.1 Age-metallicity relation in the disk