Determination of stellar ages from isochrones: Bayesian estimation versus isochrone fitting

We present a new method, using Bayesian estimation, to determine stellar ages and their uncertainties from observational data and theoretical isochrones. The result for an individual star is obtained as the relative posterior probability density as function of the age ("G function"). From this can be derived the most probable age and confidence intervals. The convoluted morphology of isochrones and strong non-linearities make the age determination by any method difficult and susceptible to statistical biases, and as a result age uncertainties havee often been underestimated in the literature. From simulations we find that the G functions provide a general, robust and reliable way to quantify age information. Resulting age estimates are at least as accurate as those obtained with conventional isochrone fitting methods, and in some cases much better, especially when the observational uncertainties are large. We also find that undetected binaries, on the whole, have a surprisingly small effect on the age determinations. For a stellar sample, the individual G functions can be combined to derive the star formation history of the population; this will be developed in a forthcoming paper. For a coeval population the combination simplifies to computing the product of the individual G functions, and we apply that method to estimate the ages of the two open clusters IC 4651 and M67, using Padova isochrones and photometric data from the literature. For IC 4651 we find an estimated age of 1.56 +/- 0.03 Gyr, assuming a true distance modulus of 9.80. For M67 we find 4.05 +/- 0.05 Gyr for true distance modulus 9.48. The small formal errors of these age estimates do not include the ( much larger) uncertainties from calibration and model errors, but illustrate the statistical power of combining G functions. Our statistical approach to the age determination problem is well suited for the mass treatment of data resulting from large-scale surveys such as the Gaia mission.