Age Mass Radius sub-WG

Context and Objectives

Accurate and precise stellar fundamental parameters are crucial towards the characterization of planetary systems. However, these are often found in the literature as the result of a case-by-case analysis conducted with a variety of approaches, thus leading to an inhomogeneous census. The goal of this sub-WG is to provide homogeneous ages, masses, and radii for Ariel target stars. This has, from the outset, been done via stellar modelling and since complemented through the use of empirical and statistical methods.

With regard to the stellar modelling approach (fully described in Bossini et al., in preparation), we have been using as reference the Bayesian tool PARAM (da Silva et al. 2006; Rodrigues et al. 2014, 2017), which matches observational constraints to a pre-computed grid of stellar models. There are two grids available to us, one of which is a MESA grid (see details in Moedas et al. 2022) that was specifically built for the modeling of Ariel targets. PARAM can use a number of inputs, namely, from spectroscopy ([Fe/H], Teff, log g), photometry (Gaia, 2MASS, AllWISE, SDSS, Tycho-2 etc.), and asteroseismology (Δν, νmax), as well as additional input (luminosity, parallax). We always make sure to iterate with the Atmospheric Parameters sub-WG in order to provide self-consistent stellar fundamental parameters (see Magrini et al. 2022; Tsantaki et al., submitted).

In order to assess the impact on the derived stellar parameters from (i) the optimisation procedure, (ii) the set of adopted observational constraints, and (iii) the choice of input physics, we have extended the set of stellar modelling tools available to the sub-WG. Five methods/teams are thus effectively involved in the modelling (namely, Porto, Graz, Paris, UCL, and Liège), each consisting in the combination of a particular optimisation procedure and evolution code. This ultimately allows evaluating the internal systematics of the results as well as the robustness of the error bars associated with each modeling tool.

As part of our strategy to gradually complement the above model-dependent stellar parameters with the use of empirical and statistical methods, we began applying empirical relations and Machine Learning (ML) techniques.

We make use of the set of empirical (linear) relations for the estimation of stellar masses and radii derived in Moya et al. (2018). Their calibration sample contains masses and radii from asteroseismology, eclipsing binaries, and interferometry. This calibration sample was deliberately chosen so as to be heterogeneous in order to reduce the influence of possible biases coming from the observations, reduction, and analysis methods used to obtain the stellar parameters.

With regard to the use of ML techniques, several regression models have been proposed in Moya & López-Sastre (2022) for estimating stellar masses and radii. The corresponding training and testing sets were derived from a sample of more than seven hundred main-sequence stars (of spectral types B to K) from the literature that have precise parameters. The model that provides the best accuracy with the least possible bias, called Stacked Generalization or Stacking, allows combining a variety of regression models and is able to improve the accuracy in mass and radius by a factor of two compared to empirical relations.

Furthermore, we have plans to compare our model-based stellar ages with (semi-)empirical ages derived from activity indices and chemical clocks, as well as to start making use of interferometric radii.