6 Element abundance ratios [Eu/Ba], [Eu/Mg], [Sr/Ba], and the evolution of the Galaxy

In this section we discuss the [Eu/Ba], [Eu/Mg] and [Sr/Ba] abundance ratios (Fig. 8) in the halo, thick and thin disk of the Galaxy. These ratios provide useful diagnostics of the role of different processes ($\alpha$-process, weak and main s-process, r-process) in the chemical enrichment of the interstellar gas and thus give important information about dominant sites of nucleosynthesis at different epochs of Galactic evolution.

There is strong evidence that the relative elemental (at least, with Z < 70) r-process abundances have not changed over the history of the Galaxy. Sneden et al. (1996) have found the elemental abundances in the extremely metal-poor star CS22892-052 ([Fe/H]  $\simeq -3.1$) consistent with the solar r-process distribution for the elements $Z \geq 56$. Similar results have been obtained for another three halo stars ([Fe/H] = -2.7 and -1.7) by Cowan et al. (1999) and for the three stars in the globular cluster M 15 ([Fe/H] = -2.2) by Sneden et al. (2000). Hill et al. (2001) studied element abundances in the range Z = 38 to Z = 92 in the halo star CS31082-001 with [Fe/H] = -2.9 and concluded that the 56 < Z < 70 elements are very well reproduced by a solar r-process. In Fig. 8 (top panel) we include a line indicating the solar abundance ratio of Eu to Ba contributed by the r-process (Arlandini et al. 1999) relative to the total abundances, [Eu/Ba]_r = 0.70. This value is uncertain within 0.1 dex mainly due to an uncertainty of the r-process contribution to $^{138}{\rm Ba}$ estimated by Arlandini et al. (1999) as 58%. To obtain the pure r-process [Sr/Ba]_r abundance ratio the contributions of the main and weak s-process to solar Sr have to be evaluated. The main s-process contributes 85% according to Arlandini et al. (1999). Up to now there is no realistic model of the weak s-process and Arlandini et al. estimate the ratio between the weak s-process and r-process contributions to solar Sr as 3:2 using the schematic approach of Beer et al. (1992). This gives [Sr/Ba] _r = -0.50, while the solar ratio of Sr contributed altogether by the r- and weak s-process to Ba contributed by the r-process, [Sr_w+r/Ba_r], equals -0.10. The last value is determined with less uncertainty of about 0.1 dex compared with 0.2 dex or even more for the [Sr/Ba]_r ratio.

Our results, apparent from Fig. 8, confirm in general and improve the conclusions drawn in Paper I; they also provide the fundaments of new conclusions.

Europium is overabundant relative to barium in halo stars with a mean value [Eu/Ba] = 0.61. We have analyzed only three halo stars and this limits us in drawing reliable conclusions concerning the halo. However, these stars complement from the side of a moderate metal-deficiency the sample of 14 extremely metal-poor stars with [Fe/H] $\leq -2.4$ studied by McWilliam (1998). Using the LTE assumption he has obtained a mean value $\rm [Eu/Ba] = 0.69$. At stellar parameters typical for his sample our NLTE calculations for Ba II and Eu II show positive NLTE abundance corrections for both elements but their values are larger for barium. So, the mean value $\rm [Eu/Ba] = 0.69$ found by McWilliam might be smaller by about 0.05-0.1 dex, and our data for the moderately metal-deficient halo stars show the same [Eu/Ba] ratio. Thus, the observed [Eu/Ba] ratios, close to ${\rm [Eu/Ba]}_r = 0.70$ independent of metallicity, favour the dominance of the r-process heavy element synthesis during the formation of the halo population. If the upper mass limit of AGB stars' progenitors, responsible for Ba synthesis in the s-process, lies between 3 $M_\odot$ (Raiteri et al. 1999) and 4 $M_\odot$ (Travaglio et al. 1999) s-nuclei of Ba appear after about 0.3-0.6 Gyr from the beginning of the protogalactic collapse. From the insignificant contribution of the s-process to Ba production we conclude that the halo population has formed rapidly during an interval of 0.3-0.6 Gyr.

Strontium is slightly underabundant relative to barium in halo stars with a mean value of [Sr/Ba] = -0.05 $\pm$ 0.06 (except for BD$34^\circ$2476). For most stars of his sample McWilliam (1998) has obtained positive or close to 0 [Sr/Ba] abundance ratios. Thus, [Sr/Ba] in halo stars is much higher compared with [Sr/Ba] _r = -0.50, and a secondary source of Sr must have occurred. Could the weak s-process be that source? Similarly to the r-process it runs in high-mass stars with an evolution time consistent with the short timescale for the halo. On the other hand, the amount of Sr produced by the weak s-process is expected to be very low in metal-poor stars simply due to the secondary nature of the weak s-process. We note that halo stars reveal [Sr/Ba] abundance ratios close to [Sr_w+r/Ba_r] = -0.10. Is this similarity accidental? Or is it because the efficiency of the weak s-process becomes more significant at [Fe/H] $\geq -2$? An alternative possibility would be that the second Sr source is the $\alpha$-rich freeze-out, as detailed by Woosley & Hoffman (1992); this mechanism is predicted to synthesize elements up to the Sr region, and as a primary process should not be extinguished at low metallicity. More theoretical work will be required to answer these questions.

Only one halo star, BD$34^\circ$2476, reveals a clear Sr underabundance relative to Ba with [Sr/Ba] = -0.34. The two CH subgiants from McWilliam's (1998) sample show [Sr/Ba] < -0.4. Does it mean these stars formed far from the weak s-process sites?

Europium is overabundant relative to barium in thick disk stars with [Eu/Ba] abundance ratios between 0.56 and 0.35. We first note a slight decline of this ratio with increasing metallicity: [Eu/Ba] reduces by about 0.1-0.15 dex as [Fe/H] grows from -1 to -0.3. This means that the r-process remained dominant in heavy element production during thick disk evolution. At the same time, evolved low mass stars started to enrich the interstellar gas by s-nuclei of Ba. The decrease of the [Eu/Ba] ratio by 0.1-0.15 dex constitutes a constraint to the duration of that phase. From the small contribution of the s-process to Ba production we conclude that, similar to the halo, the thick disk population formed in the early Galaxy, when high mass stars were the main sites of nucleosynthesis. Keeping in mind the evolution time of AGB star progenitors we suppose that the duration of halo and thick disk formation was not much longer than 1 Gyr. This conclusion is in good agreement with ages of the three thick disk subgiants of our sample obtained by Bernkopf et al. (2001) on the base of recently improved stellar interior calculations. Bernkopf et al. (2001) give 13.8 $\pm$ 1.3 Gyr, 13.5 $\pm$ 1.3 Gyr and 12.5 $\pm$ 1.1 Gyr for the thick disk subgiants HD3795, HD10519 and HD222794, respectively. It is also compatible with age estimates for halo stars based on the detection of the Th II $\lambda$4019 line in spectra of very metal-poor stars of Sneden et al. (1996) and Cowan et al. (1999) who have obtained an average age of 15.6 $\pm$ 4.6 Gyr for the two stars CS22892-052 ([Fe/H]  $\simeq -3.1$) and HD115444 ([Fe/H] $\simeq -2.7$); Sneden et al. (2000) also have determined an age of 14 $\pm$ 3 Gyr for the stars in M 15. Recently Cayrel et al. (2001) have detected the U II $\lambda$3859.57 line in the very metal-poor star CS31082-0018, and using uranium abundance as a cosmochronometer have estimated an age of this star as 12.5 $\pm$ 3 Gyr. As Spite (2001) kindly informed us, the gf-value of the U II line has been revised since the publication of Cayrel et al. (2001) result and the age is now 13.2 $\pm$ 2 Gyr. Thus, within error bars the thick disk stellar population is as old as the halo. We note further that the halo and thick disk stars' ages agree well with the recent cosmological age estimates, based on high-redshift supernovae, of 14.9 $\pm$ 1.5 Gyr (Perlmutter et al. 1999) and 14.2 $\pm$ 1.7 Gyr (Riess et al. 1998).

Strontium is slightly overabundant relative to barium in the thick disk stars with the mean value [Sr/Ba] = 0.05 $\pm$ 0.05. This could be due to a strengthening of the weak s-process with increasing overall metallicity. Theoretical studies of the weak s-process are required to test this idea.

This study confirms the step-like decrease of the [Eu/Ba] abundance ratio at the thick-to-thin disk transition found in our previous analysis (Paper I). In the region of overlapping metallicities the [Eu/Ba] ratios in the thin disk stars are lower on average by 0.25 dex compared with the thick disk stars. This finding is indicative of a phase of ceased star formation before the onset of the thin disk formation during which r-process element production stopped but s-process nuclei of Ba were synthesized in evolved low mass stars. The duration of this intermediate phase can be evaluated from calculations of the s-process nucleosynthesis in AGB stars, and our [Ba/Fe] (Fig. 1) and [Eu/Ba] (Fig. 8) ratios provide observational constraints. Such a hiatus in star formation was suggested by Gratton et al. (1996) and Fuhrmann (1998) on the base of the [$\alpha$/Fe] abundance ratio analyses. Direct evidence of a star formation gap between thick and thin disk of no less than 3 Gyr is given by Bernkopf et al. (2001). They have obtained stellar ages between 6.8 and 8.1 Gyr for the three thin disk subgiants and between 12.5 and 13.8 Gyr for the thick disk subgiants mentioned above. Thus, from the point of view of their chemical history and age the thick disk stellar population is much closer to the halo than to the thin disk stellar population. The thin disk stars show a steep decline of the [Eu/Ba] abundance ratios with increasing metallicity: [Eu/Ba] is reduced by about 0.35 dex as one goes from $\rm [Fe/H] = -0.5$ to 0.25. These data indicate that evolved low mass stars now produce larger masses of s-process elements as compared with the return of r-elements from high mass stars, well in agreement with the thin disk IMF and the long timescale of about 9 Gyr. Sr nearly follows Ba in the thin disk stars and this confirms again that the main s-process now becomes dominant in the production of these elements.

In Paper I we have first reported an overabundance of Eu relative to Mg in two halo stars. One halo star added in this study, HD103095, shows the same overabundance with [Eu/Mg] = 0.27. Moreover, there is a marginal tendency towards a higher [Eu/Mg] ratio in the "early'' thick disk stars (the mean value [Eu/Mg] = 0.04 $\pm$ 0.05 at [Fe/H] < -0.65) compared with the "late'' thick disk stars (the mean value [Eu/Mg] = -0.05 $\pm$ 0.04 at the near solar Mg abundances, except for HD3795 with [Eu/Mg] = 0.17).

The knowledge of the [Eu/Mg] abundance ratio in the oldest stars of the Galaxy is of great importance for an estimate of the timescale for early Galaxy formation. Theoretical predictions of SN II element yields show that [$\alpha$/Fe] increases with increasing progenitor mass (Arnett 1991). Most theoretical models of r-process nucleosynthesis are based on low mass (8-12 $M_\odot$) supernovae (Mathews & Cowan 1990; Tsujimoto & Shigeyama 1998; Travaglio et al. 1999). Ishimaru & Wanajo (1999) constrain the mass range of SNe for the r-process site by either 8-10 $M_\odot$ or $\geq\!30~{M}_\odot$. If the production of Eu is related to low mass SNe while Mg is produced in larger amounts in high-mass SNe we should expect an underabundance and, certainly, not an overabundance of Eu relative to Mg in the oldest stars of the Galaxy. We have inspected europium and magnesium abundances available in the literature. For a sample of 12 halo stars with [Fe/H] from -2.66 to -1.48 from Magain's (1989) work the [Eu/Mg] abundance ratios vary from -0.01 to 0.51 with the mean value [Eu/Mg] = 0.18. Only one star, HD140283, shows an underabundance of Eu relative to Mg of 0.30 dex, however, for the same star Ryan et al. (1996) give [Eu/Mg] = 0.33. A surprisingly large spread in [Eu/Mg] can be found in the McWilliam et al. (1995) and Ryan et al. (1996) data for very metal-poor stars. In the first paper the [Eu/Mg] ratios vary from -0.52 to 1.95 for the sample of 14 stars and in the second one from 0.15 to 1.86 for a sample of 12 stars with one star revealing [Eu/Mg] = -1. At the same time, we note a large divergence of elemental abundances between these two studies for stars in common. For example, for CS22952-015 ([Fe/H $\simeq$ -3.4) McWilliam et al. and Ryan et al. obtain [Mg/Fe] = -0.18 and 0.38, respectively; for CS22968-014 ([Fe/H $\simeq$ -3.4) [Mg/Fe] = -0.06 and 0.64; for CS22885-096 ([Fe/H $\simeq$ -3.8) Ryan et al. find an overabundance of Eu relative to Fe of 1 dex while McWilliam et al. cannot even measure the Eu II lines. Thus, much more observational work will be required to improve europium to magnesium abundance ratios in halo stars. A large spread in [Eu/Mg] for very metal-poor stars, if it exists, indicates different sites for Mg and Eu production and quite insufficient mixing of the interstellar gas in the early Galaxy.

As our sample of halo stars is small (3 stars) we can draw only a preliminary conclusion that our data on the [Eu/Mg] abundance ratios in the halo and "early'' thick disk stars complemented by the data available in the literature do not support theoretical models of the r-process based on low mass SNe. Assume that Eu is mostly produced in the higher mass SNe compared with Mg. In this case a timescale for the galactic halo is defined by a time delay of SNe II producing Mg and it cannot be larger than 20 million years which is the evolution time of 8 $M_\odot$ mass star (Massevich & Tutukov 1988). Therefore the halo formation phase may indeed be much shorter than the 0.3-0.6 Gyr deduced above from the analysis of the [Eu/Ba] abundance ratios.

Summing up the above results we imagine the following scenario of the Galaxy evolution. The first stellar population of the Galaxy consisted of very high-mass stars and produced heavy elements with a higher efficiency for the r-process elements compared with $\alpha-$elements or iron. Thus the interstellar gas, out of which the second stellar population (halo) formed, had [Eu/Mg] > 0, [Eu/Fe] > 0 and [Mg/Fe] > 0. The halo stellar population formed during a very short interval comparable to the evolution time of progenitors of those SNe II responsible for Mg production. The question then is: what are masses of these progenitors? The halo formation was characterized by a very high star formation rate. During this phase r-, $\alpha$-elements and iron were produced with nearly the same efficiency and, probably, in common sites, so that the [Mg/Fe], [Eu/Fe] and [Eu/Mg] ratios kept their values. Until the onset of thick disk formation the progenitors of SNe II, which are the major producers of magnesium, have evolved and the [Eu/Mg] abundance ratio decreases in the "early'' thick disk stars (Fig. 8, bottom panel). As the evolution time of SNe II progenitors is not longer than 20 million years therefore the onset of the thick disk refers to the early Galaxy. The timescale for the thick disk formation is probably of the order of 1 Gyr. During this phase iron starts to be produced in SNe I and its production rate is higher than that for Eu resulting in a steep decline of [Eu/Fe] with [Fe/H] (Fig. 2, top panel); the production rate of iron is also higher than for Mg (there is evidence of a slight decline of the [Mg/Fe] and [$\alpha$/Fe] abundance ratios with metallicity in the figures of Bernkopf et al. 2001; Prochaska et al. 2000). The heavy elements beyond the iron group are mainly produced by the r-process in high mass SNe II, however, the main s-process nuclei appear. The decrease of the [Eu/Ba] ratio by about 0.1-0.15 dex implies a constraint to the duration of the thick disk formation phase. Then star formation in our Galaxy stopped for about 3 Gyr (according to Bernkopf et al. 2001). Europium abundances [Eu/H] (Fig. 2, bottom panel) and Mg abundances [Mg/H] (Bernkopf et al. 2001) remained constant during this phase while iron and the main s-process elements such as Ba continued to be produced in evolved lower-mass stars. The decrease by about 0.25 dex of the [Eu/Ba] ratio at the thick-to-thin disk transition provides an independent method to estimate the duration of that intermediate phase. The thin disk phase then was characterized by the higher iron production rate compared with that for $\alpha$- (Fuhrmann 1998) and r-elements (Fig. 2, top panel). In turn, the main s-process elements were produced during this phase with a larger efficiency compared with iron (Table 2).

The suggested scenario based on the chemical history of the Galaxy will be useful to develop a realistic model of the Galaxy evolution taking into consideration physical and dynamical parameters of the galactic stellar populations. One of the important and unsolved problems of the Galaxy's chemical evolution concerns the astrophysical site for the r-process; it requires further work in stellar evolution, nuclear physics and stellar spectroscopy. Yet it is somewhat surprising that 40 years after the trailblazing work of Eggen et al. (1962) we return to very much the same conclusions, however, with at least one more population than was known at that time.

Acknowledgements

M. L. acknowledges with gratitude the Max-Planck-Institut of Astrophysics for the partial support of this study and the Institute of Astronomy and Astrophysics of Munich University for warm hospitality during a productive stay in July-September 2000. M. L. thanks especially Rolf-Peter Kudritzki for his support. We thank Klaus Fuhrmann for providing reduced FOCES spectra and parameters for most of the stars investigated in this paper, for valuable help and useful discussions, and for comments on the manuscript of this paper. We are grateful to Andreas Korn for providing reduced FOCES spectra and parameters for the three stars and to Johannes Reetz for providing the SIU code for synthetic spectrum computations. We report with sorrow the death of Michael Pfeiffer who designed and built the échelle spectrograph FOCES, on which our present results are based. M. L. has been partially supported by the Russian Basic Researches Fund (grant 99-02-17488).