Accuracy of spectroscopy-based radioactive dating of stars

H.-G. Ludwig^1,2, E. Caffau², M. Steffen³, P. Bonifacio^1,2,4 and L. Sbordone^1,2

¹ CIFIST Marie Curie Excellence Team, France e-mail: Hans.Ludwig@obspm.fr
² GEPI, Observatoire de Paris, CNRS, Université Paris Diderot, Place Jules Janssen, 92190 Meudon, France
³ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
⁴ Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italy

Received: 10 August 2009
Accepted: 7 October 2009

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 .

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.