Asteroseismic age estimates of RGB stars in open clusters

Abstract

Context. Open clusters (OCs) provide a classical target to calibrate the age scale and other stellar parameters. Despite their wide use, some issues remain to be explored in detail. Aims. We performed a theoretical investigation focused on the age estimate of red giant branch (RGB) stars in OCs based on mixed classical surface (Teff and [Fe/H]) and asteroseismic (Δν and νmax) parameters. We aimed to evaluate the performances of three widely adopted fitting procedures, that is, a pure geometrical fit, a maximum likelihood approach, and a single stars fit, in recovering stellar parameters. Methods. A dense grid of stellar models was computed, covering different chemical compositions and different values of the mixing-length parameter. Artificial OCs were generated from these data 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 cluster age and other fundamental parameters were then recovered by means of the three methods previously mentioned. A Monte Carlo Markov chain approach was adopted for estimating the posterior densities of probability of the estimated parameters. Results. 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 value of the initial helium content was recovered unbiased within the large random errors on the estimates. The maximum likelihood 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 owing to its neglect of the fact that the stars came from the same cluster. The age of the cluster was recovered with no biases for 7.5 Gyr true age and with a bias of −0.4 Gyr for 9.0 Gyr. The most important difference between geometrical and maximum likelihood approaches was the robustness against observational errors. For the first fitting technique, we found that estimations starting from the same sample but with different Gaussian perturbations on the observables suffer from a variability in the recovered mean of about 0.3 Gyr from one Monte Carlo run to another. This value was as high as 45% of the intrinsic variability due to observational errors. On the other hand, for the maximum likelihood fitting method, this value was about 65%. This larger variability led most simulations – up to 90% – to fail to include the true parameter values in their estimated 1σ 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. Conclusions. Each method has its own merits and drawbacks. The single star fit showed the lowest performances. The higher precision of the maximum likelihood estimates is partially negated by the lower protection that this technique shows against random fluctuations compared to the pure geometrical fit. Ultimately, the choice of the fitting method has to be evaluated in light of the specific sample and evolutionary phases under investigation.

Mixing-length calibration from field stars

“…A much better result from empirical calibrations can be reached by relying on cluster stars (see e.g. Palmieri et al 2002;Yıldız et al 2008;Basu et al 2010;Valle et al 2018c). In this case it is possible to reduce the error in the estimates largely by assuming a common chemical composition and a common age for all the stars.…”

Impact of measurement errors on the inferred stellar asteroseismic ages

“…For age recovery the widely adopted pure geometrical isochrone fitting method was employed (see Valls-Gabaud 2014, and references therein), as described in Valle et al (2018). For readers' convenience we summarize here the method.…”

“…A possible proposed remedy is to factorize in the likelihood computation the evolutionary time step (see e.g. the discussion in Valls-Gabaud 2014; Valle et al 2018), but direct verification for RGB phase showed that this alternative approach has its own difficulties because it can provide biased estimates (Valle et al 2018).…”

Goodness-of-fit test for isochrone fitting in the Gaia era. Statistical assessment of the error distribution

“…The direct computation of the minimum distance between the isochrone support points and P is known to pose several problems (see e.g. Frayn & Gilmore 2002;Valle et al 2018). In the following, the minimum distance is computed by approximating I with a straight line t between two consecutive points and evaluating the minimum distance between t and P. This approximation is known to be very good as the errors introduced by the linear approximation are totally negligible (see e.g.…”

“…They also provide a classical target for calibrating the age scale and other stellar parameters such as the initial helium abundance, superadiabatic convection efficiency, or the convective core overshooting parameter (see e.g. VandenBerg & Stetson 2004;Gennaro et al 2012;Valle et al 2018;McKeever et al 2019;Tognelli et al 2021).…”