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

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: $M=1.51 \pm 0.05 M_\odot$, $X_c =0.43 \pm 0.04$, $R=1.66 \pm 0.1 R_\odot$, $f_{\rm ov}=0.010$, $Ω_c=1.58 \pm 0.01$ 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 $γ$ 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.