KIC 4150611: A quadruply eclipsing heptuple star system with a g-mode period-spacing pattern Asteroseismic modelling of the g-mode period-spacing pattern

TL;DR

This study uses asteroseismic analysis with neural networks and MCMC methods to precisely determine the stellar parameters of a primary star in a complex star system, confirming its properties and age.

Contribution

It introduces a novel combination of neural network-based asteroseismic modelling with classical MCMC analysis for detailed stellar parameter estimation.

Findings

Stellar parameters for Aa are precisely estimated and consistent with external constraints.

Aa is a typical gamma Dor star with near-rigid rotation.

Asteroseismic age (1100 Myr) is older than previous isochrone estimates.

Abstract

In this work, we aim to estimate the stellar parameters of the primary (Aa) by performing asteroseismic analysis on its period-spacing pattern. We use the C-3PO neural network to perform asteroseismic modelling of the g-mode period-spacing pattern of Aa, discussing the interplay of this information with external constraints from spectroscopy ($T_{\rm eff}$ and $\log(g)$) and eclipse modelling ($R$). To estimate the level of uncertainty due to different frequency extraction and pattern identification processes, we consider four different variations on the period-spacing patterns. To better understand the correlations between and the uncertainty structure of our parameter estimates, we also employed a classical, parameter-based MCMC grid search on four different stellar grids. The best-fitting, externally constrained model to the period-spacing pattern arrives at estimates of the stellar properties for Aa of: $M=1.51 \pm 0.05 M_\odot$, $X_c =0.43 \pm 0.04$, $R=1.66 \pm 0.1 R_\odot$, $f_{\rm ov}=0.010$, $\Omega_c=1.58 \pm 0.01$ d$^{-1}$ with rigid rotation to within the measurement errors, $\log(T_{\rm eff})=3.856 \pm 0.008$ dex, $\log(g)=4.18 \pm 0.04$ dex, and $\log(L)=0.809 \pm 0.005$ dex, which agree well with previous measurements from eclipse modelling, spectroscopy, and the Gaia DR3 luminosity. We find that the near-core properties of the best-fitting asteroseismic models are consistent with external constraints from eclipse modelling and spectroscopy. Aa appears to be a typical example of a $\gamma$ Dor star, fitting well within existing populations. We find that Aa is quasi-rigidly rotating to within the uncertainties, and note that the asteroseismic age estimate for Aa (1100 $\pm$ 100 Myr) is considerably older than the young (35 Myr) age implied by previous isochrone fits to the B binary in the literature. Our MCMC parameter-based grid-search agrees well with our pattern-modelling approach.