Accuracy of spectroscopy-based radioactive dating of stars

Abstract

Context: 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. Aims: We quantify the uncertainties arising from the spectroscopic analysis, and compare these to the other error sources. Methods: 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. Results: 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 √N. Conclusions: 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. © 2010 ESO.