Impact of measurement errors on the inferred stellar asteroseismic ages. Statistical models for intermediate age main sequence and red giant branch stars

Abstract

We theoretically quantify the impact of observational errors on the recovered age for stars in MS and RGB phases. We adopted Teff, [Fe/H], Delta_nu and nu_max as observational constraints. Artificial stars were sampled from a reference isochrone and subjected to random perturbation to simulate observational errors. Their ages were then recovered by means of a MCMC approach. The differences between the recovered and true ages were modelled against the errors in the observables by means of linear models and projection pursuit regression models. From linear models we find that no age error source dominates. For MS the most important error source is Teff. An offset of 75 K accounts for an underestimation of the stellar age from 0.4 to 0.6 Gyr for initial and terminal MS. An error of 2.5% in nu_max accounted for about -0.3 Gyr. A 0.1 dex error in [Fe/H] resulted particularly important only at the end of the MS, with an age error of -0.4 Gyr. For the RGB phase the dominant source of uncertainty is nu_max, causing an underestimation of about 0.6 Gyr; the offset in the effective temperature and Delta_nu caused respectively an underestimation and overestimation of 0.3 Gyr. We find that the inference from the linear model is a good proxy for that from projection pursuit regression models, so that linear models can be safely used thanks to its broader generalizability. Finally, we explored the impact on age estimates of adding the luminosity to the other observational constraints. We assumed - for computational reasons - a 2.5% error in luminosity, much lower than the average error in the Gaia DR2 catalogue. Even in this optimistic case, the luminosity does not increase precision of age estimates. Moreover, the luminosity resulted as a major contributor to the variability in the estimated ages, accounting for an error of about -0.3 Gyr in the explored evolutionary phases.

Accepted for publication in A&A. Abstract abridged

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