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

TL;DR

This paper introduces a hierarchical Bayesian approach to improve stellar parameter inference from asteroseismology by statistically modeling helium abundance and mixing-length parameters across a star population, reducing uncertainties.

Contribution

The study develops a novel hierarchical Bayesian model that accounts for population-level distributions of key stellar parameters, enhancing the accuracy of individual star property estimates.

Findings

Estimated helium enrichment law gradient: ΔY/ΔZ ≈ 1.05

Derived mean mixing-length parameter: μ_α ≈ 1.90

Achieved 2.5% mass and 1.2% radius uncertainties

Abstract

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 ($\alpha_\mathrm{MLT}$) 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 ($0.8 < M < 1.2\,\mathrm{M_\odot}$). In this method, we include a statistical treatment of $Y$ and the $\alpha_\mathrm{MLT}$. We develop a hierarchical Bayesian model to encode information about the distribution of $Y$ and $\alpha_\mathrm{MLT}$ in the population, fitting a linear helium enrichment law including an intrinsic spread around this relation and normal distribution in $\alpha_\mathrm{MLT}$. 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, $\Delta Y / \Delta Z = 1.05^{+0.28}_{-0.25}$ and the mean $\alpha_\mathrm{MLT}$ in the population, $\mu_\alpha = 1.90^{+0.10}_{-0.09}$. While accounting for the uncertainty in $Y$ and $\alpha_\mathrm{MLT}$, 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 which will lead to improved constraints on both the population level inference and the star-by-star fundamental parameters.