4. The age of the stars
So far, we have been evaluating the stellar ages on the basis of a fit to the solar r-abundance distribution. Such a procedure is obvioulsy based on our initial fundamental assumption that the r-process site is unique in the Galaxy. This basic assumption is a fundamental prerequisite to build a Th cosmochronometry upon the abundance analysis of metal-poor stars at the present time, since, as explained above, a direct fit to the abundance distribution observed at the surface of metal-poor stars would present even larger uncertainties, because of the restricted number of elements observed, the impossibility to distinguish isotopic ratios and the much smaller accuracy in the abundance data as compared with our solar system. However, in the specific case of Pb, the uncertainties still affecting the solar abundance might be greater than the ones found in the observation at the surface of HD 115444 or HD 126238 (Sneden et al. 1998), so that the Pb abundance in such stars could probably be more constraining on the Th predictions than the solar value. Unfortunately, the Th abundance has not been determined yet in such stars, so that in this case, we limit the discussion on the relative stellar age. Compared with CS 22892-052, only a small number of r-elements are observed in HD 115444, but it is at the moment the only metal-poor star in which Pb and Th lines are detected simultaneously. All the physically sound (i.e leading to a positive age ) calculations presented in the previous section are compared, in Fig. 6, with the elemental abundance distribution observed in HD 115444 and CS 22892-052. We only retain calculations which provide a good fit to the observed abundances, and in particular to the Pb abundance in the case of HD 115444. In order to achieve a good fit to all elements observed and to optimize the extrapolation to the Th region, a normalization of the abundance curves is done on the heaviest elements accurately observed, i.e Pt and Os for HD 115444 and CS 22892-052, respectively. In this case, the age of CS 22892-052 is found to lie in the range, and a similar error range of about 32 Gyr is predicted for the age of HD 115444. The different predictions of the stellar age, as well as the elemental abundances of Eu, Pb, Bi, Th and U are summarized in Table 1. The stellar age can be determined in two different ways. If normalized to the calculated Eu abundance, the age has the advantage of beeing free from uncertainties in the normalization procedures on the observed abundances, but is sensitive to the theoretical uncertainties made in the r-process predictions. In particular, it is well known that the origin of the r-nuclides in the region is not easily explainable (e.g Meyer & Mullenax 1998). The impact of such errors remains to be estimated. On the contrary, normalizing the calculated Th abundance on the observed Eu avoids theoretical complications inherent in the origin of the nuclides, but gives rise to additional errors of the order of dex on the abundances (as seen in Fig. 6), i.e of Gyr on the age .
Table 1. Ages (in Gyr) of CS 22892-052, elemental abundances (in log) for Eu, Pb, Bi, Th, U and log(Th/U) predicted by the different theoretical calculations shown in Fig. 6 and analyzed in Sect. 3. () corresponds to the age calculated with a Th abundance normalized to the calculated (observed) Eu abundance.
Although the present study suggests that at the moment great care should be taken in estimating the age of the stars on the basis of observed Th abundance, new accurate observations of heavy r-elements could put the Th cosmochronometry on safer grounds, especially if Th and U lines could be observed accurately and simultaneously in metal-poor stars, as already stressed by Arnould & Takahashi (1999). As a matter of fact, if the Th and U lines are available, an age estimate could be derived from the expression
where is the characteristic -decay timescale of U. As seen in Fig. 6 and Table 1, is found to lie within an 0.1 range, whatever theoretical inputs are used in the r-process model. Such an accurate estimate is principally bound to the fact that Th and U are neighbour nuclei, and consequently their production ratio is not strongly affected by unreliable extrapolation procedures, but rather by local nuclear uncertainties, such as nuclear masses or fission processes in the actinide region.
From Eq. (2), it is found that a error on the observed or predicted production ratio of Th/U gives rise to a Gyr error on . A future simultaneous observation of Th and U lines in ultra-metal-poor stars could therefore open the way to an accurate age determination in contrast to the still complicated Th cosmochronometry based on Th lines only. Eq. (2) is shown in a graphical form in Fig. 7 for 3 possible values of the Th/U production ratio. Note, however, that a deeper analysis of the Th/U production ratio would be required before rushing into an age determination. In particular, uncertainties in the fission processes have not been included in the present study, but could possibly affect the predicted Th/U ratio.
© European Southern Observatory (ESO) 1999
Online publication: June 17, 1999