6 The age of CS 31082-001

The very low metallicity of CS 31082-001, well below that of the most metal-poor globular clusters, shows that it was formed in the earliest star formation episodes, either in the Galaxy or in a substructure which later merged with the Galaxy. Comparison with the metallicity of damped Ly-$\alpha$ systems at high redshift (Lu et al. 1996; Vladilo et al. 2000) shows that the matter in CS 31082-001 probably originated at an epoch earlier than z=5. Assuming $\Omega _0=0.3$, H₀ in the plausible range 65-75 km s^-1/Mpc, and a flat geometry (de Bernardis et al. 2000), the Big Bang occurred about 0.5 Gyr before the epoch z=10, and 1 Gyr before z=5. Accordingly, the age of the progenitor of CS 31082-001, as determined from the U/Th clock, provides a lower limit to the age of the Universe which is very close to that age itself.

Dating matter from the decay of a radioactive isotope is simple in principle, provided that the ratio of the radioactive nuclide to a stable reference element produced at the same time can be inferred. Let (R/S)₀be the initial production ratio of a radioactive nuclide, R, to a stable one, S, and (R/S) $_{{\rm now}}$ be the value of that ratio observed today. The time for R/S to decay by a factor of 10 is then $\tau_{10} = \tau / \log (2)$, where $\tau$ is the half-life of R. For ²³²Th and ²³⁸U ($\tau$= 14.05 and 4.47 Gyr, respectively), this yields the following expressions for the time $\Delta t$ (in Gyrs) elapsed since the production of these elements:

$$% \Delta t = 46.67[\log(\mathrm{Th/S}_0)-\log(\mathrm{Th/S}_{{\rm now}})]$$ (1)

$$% \Delta t =14.84[\log(\mathrm{U/S}_0)-\log(\mathrm{U/S}_{{\rm now}})].$$ (2)

These relations show that, if the right-hand sides can be evaluated to a realistic accuracy of 0.1 dex, the corresponding error on $\Delta t$ becomes 4.7 Gyr for Th and 1.5 Gyr for U, demonstrating immediately the huge advantage of U over the previously used Th in cosmochronometry. However, finding a stable r-process element that permits a spectroscopic determination of $(R/S)_{{\rm now}}$ and a theoretical prediction of (R/S)₀, with a combined overall error of 0.1 dex is a significant, unsolved problem.

Hence, we look to an obvious alternative. Substituting Th for the stable element S in Eq. (2) above, we obtain:

$$% \Delta t =21.76[\log(\mathrm{U/Th}_0)-\log(\mathrm{U/Th}_{{\rm now}})].$$ (3)

Thus, for a given uncertainty in the decay of the U/Th ratio, the error in $\Delta t$ is 50% larger than for U alone, but still a factor of two better than for Th alone. Adopting the slightly radioactive, but structurally very similar Th, as the reference element for U leads to great gains in accuracy of both terms on the right-hand side of Eq. (3). First, the ionization and excitation potentials of the atomic levels giving rise to the observed spectral lines are similar, so that errors in the model atmospheres and assumed parameters largely cancel in the ratio U/Th (see Table 6). Second, the initial production ratio of the neighboring nuclides ²³⁸U and ²³²Th should be far less sensitive to variations in the poorly-known characteristics of the neutron exposure(s) occurring in the explosion of progenitor than the ratios of nuclides more widely separated in mass, such as ²³²Th and ^151-153Eu (Goriely & Clerbaux 1999).

Much progress has already been made on both fronts since the publication of our discovery paper (Cayrel et al. 2001). First, the oscillator strengths of the single U II line and eight of the Th II lines that we have measured in CS 31082-001 have been re-determined (Sect. 4.5). The change in the U/Th abundance ratio is quite significant, revising the $\log$(U/Th) from the previous value of -0.74 $\pm$ 0.15 to -0.94 $\pm$ 0.11. Using the same initial production ratio as in Cayrel et al. (2001), this leads to an age of almost 17 Gyr, 4.3 Gyr greater than that originally published. By contrast, use of the conventional Th/Eu chronometer (Cowan et al. 1999) leads instead to a slightly negative (!), or at most a T-Tauri like age for CS 31082-001.

Fortunately, there has also been progress regarding predictions of the initial production ratio for these elements. In a recent paper, Goriely & Arnould (2001) review in great detail the production of the actinides in the light of the Solar System data. Although they conclude that no current solution explains the Solar System data exactly, stretching the lower and upper limits of the production ranges by just 0.1 dex makes 10 of the 32 cases they consider acceptable. The corresponding production ratios range from 0.48 to 0.54, with a mean of $0.50 \pm 0.02$, close to the value of 0.556 (from Cowan et al. 1999) cited by Cayrel et al. (2001). Combined with our newly measured U/Th ratio, this leads to an age of $14.0\pm 2.4$ Gyr for the Th and U in CS 31082-001 (where the error refers only to the uncertainty on the observed U/Th ratio). This is a quite reasonable value, inspiring some hope that the predicted production ratio of U/Th is fairly robust.

At this point, it is impossible to assign a reliable error estimate to this age, given the lack of observational constraints on the production ratio of U/Th from other species that might have experienced the same neutron exposure. Verification of the predicted abundances of the decay products Pb and Bi, the direct descendants of U and Th, is therefore of particular importance. No useful lines of these elements are measurable, even in our high-quality VLT/UVES spectra of CS 31082-001, and we suspect that they may remain unmeasurable, regardless of improvements in future ground-based facilities. Fortunately, time on the Hubble Space Telescope has been assigned to obtain a high-resolution UV spectrum of CS 31082-001, where the strong resonance lines of these species might indeed be detected.

Let us note also that using the upper limit $\log \epsilon{\rm (U)} \leq -2.54$ of Gustafsson & Mitzuno-Wiedner (2001, modified to account for the new gf of the U line) for uranium in CS 22892-052, and the thorium abundance $\log \epsilon{\rm (Th)} =-1.60$ of Sneden et al. (2000a), the ratio U/Th $\leq -$0.94 in CS 22892-052 is fully compatible with the one of CS 31082-001. Hence, despite a difference in the overall thorium content of the two stars, their ages derived from the U/Th ratio is fully consistent.