Hierarchically modelling Kepler dwarfs and subgiants to improve inference of stellar properties with asteroseismology

With recent advances in modelling stars using high-precision asteroseismology, the systematic effects associated with our assumptions of stellar helium abundance (Y) and the mixing- length theory parameter (α_MLT) are becoming more important. We apply a new method to improve the inference of stellar parameters for a sample of Kepler dwarfs and subgiants across a narrow mass range (0.8 M 1.2 M_⊙). In this method, we include a statistical treatment of Y and the α_MLT. We develop a hierarchical Bayesian model to encode information about the distribution of Y and α_MLT in the population, fitting a linear helium enrichment law including an intrinsic spread around this relation and normal distribution in α_MLT. We test various levels of pooling parameters, with and without solar data as a calibrator. When including the Sun as a star, we find the gradient for the enrichment law, Δ Y / Δ Z = 1.05+0.28­0.25 and the mean α_MLT in the population, μ _α = 1.90+0.10­0.09. While accounting for the uncertainty in Y and α_MLT, we are still able to report statistical uncertainties of 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Our method can also be applied to larger samples that will lead to improved constraints on both the population level inference and the star- by-star fundamental parameters.