Isochrone ages for field dwarfs: method and application to the age–metallicity relation

A new method is presented to compute age estimates from theoretical isochrones using temperature, luminosity and metallicity data for individual stars. Based on Bayesian probability theory, this method avoids the systematic biases affecting simpler strategies and provides reliable estimates of the age probability distribution function for late-type dwarfs. Basic assumptions concerning the a priori parameter distribution suitable for the solar neighbourhood are combined with the likelihood assigned to the observed data to yield the complete posterior age probability. This method is especially relevant for G dwarfs in the 3–15 Gyr range of ages, crucial to the study of the chemical and dynamical history of the Galaxy. In many cases, it yields markedly different results from the traditional approach of reading the derived age from the isochrone nearest to the data point. We show that the strongest process affecting the traditional approach is that of strongly favouring computed ages near the end-of-main-sequence lifetime. The Bayesian method compensates for this potential bias and generally assigns much higher probabilities to lower main-sequence ages, compared with short-lived evolved stages. This has a strong influence on any application to galactic studies, especially given the present uncertainties on the absolute temperature scale of the stellar evolution models. In particular, the known mismatch between the model predictions and the observations for moderately metal-poor dwarfs (−1 < [Fe/H] < −0.3) has a dramatic effect on the traditional age determination. We apply our method to the classic sample of Edvardsson et al., who derived the age–metallicity relation (AMR) of 189 field dwarfs with precisely determined abundances. We show how much of the observed scatter in the AMR is caused by the interplay between the systematic biases affecting the traditional age determination, the colour mismatch with the evolution models and the presence of undetected binaries. Using new parallax, temperature and metallicity data, our age determination for the same sample indicates that the intrinsic dispersion in the AMR is at most 0.15 dex and probably lower. In particular, we show that old, metal-rich objects ([Fe/H]∼ 0.0 dex, age > 5 Gyr) and young, metal-poor objects ([Fe/H] < −0.5 dex, age < 6 Gyr) in many observed AMR plots are artefacts caused by too simple a treatment of the age determination. The incompatibility of those AMR plots with a well-mixed interstellar medium may therefore only be apparent. Incidentally, our results tend to restore confidence in the method of age determination from the chromospheric activity for field dwarfs.