Asteroseismic age estimates of RGB stars in open clusters. A statistical investigation of different estimation methods.

We performed a theoretical investigation focused on the age estimate of RGB stars in OCs based on mixed classical surface and asteroseismic parameters. We evaluated the performances of three widely adopted methods (pure geometrical fit, maximum likelihood approach, and a single stars fit) in recovering stellar parameters. Artificial OCs were generated by means of a Monte Carlo procedure for two different ages (7.5 and 9.0 Gyr) and two different choices of the number of stars in the RGB evolutionary phase (35 and 80). The geometrical approach overestimated the age by about 0.3 and 0.2 Gyr for true ages of 7.5 and 9.0 Gyr, respectively. The ML approach provided similar biases (0.1 and 0.2 Gyr) but with a variance reduced by a factor of between two and four with respect to geometrical fit. The independent fit of single stars showed a very large variance. The most important difference between geometrical and ML approaches was the robustness against observational errors. For the geometrical method, we found that estimations starting from the same sample but with different Gaussian perturbations on the observables had about 0.3 Gyr random variability from one Monte Carlo run to another (45% of the intrinsic variability due to observational errors). On the other hand, for the ML method, this value was about 65% and 90% of the simulations failed to include the true parameter values in their estimated 1 sigma credible interval. Finally, we compared the performance of the three fitting methods for single RGB-star age estimation. The variability owing to the choice of the fitting method was minor, being about 15% of the variability caused by observational uncertainties.