Accuracy of spectroscopy-based radioactive dating of stars

Combined spectroscopic abundance analyses of stable and radioactive elements can be applied for deriving stellar ages. The achievable precision depends on factors related to spectroscopy, nucleosynthesis, and chemical evolution. We quantify the uncertainties arising from the spectroscopic analysis, and compare these to the other error sources. We derive formulae for the age uncertainties arising from the spectroscopic abundance analysis, and apply them to spectroscopic and nucleosynthetic data compiled from the literature for the Sun and metal-poor stars. We obtained ready-to-use analytic formulae of the age uncertainty for the cases of stable+unstable and unstable+unstable chronometer pairs, and discuss the optimal relation between to-be-measured age and mean lifetime of a radioactive species. Application to the literature data indicates that, for a single star, the achievable spectroscopic accuracy is limited to about +/- 20% for the foreseeable future. At present, theoretical uncertainties in nucleosynthesis and chemical evolution models form the precision bottleneck. For stellar clusters, isochrone fitting provides a higher accuracy than radioactive dating, but radioactive dating becomes competitive when applied to many cluster members simultaneously, reducing the statistical errors by a factor sqrt(N). Spectroscopy-based radioactive stellar dating would benefit from improvements in the theoretical understanding of nucleosynthesis and chemical evolution. Its application to clusters can provide strong constraints for nucleosynthetic models.