  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.
