KIC 4150611: A quadruply eclipsing heptuple star system with a

Context. KIC 4150611 is a high-order (seventh-order) multiple composed of a triple system with: a F1V primary (Aa), which is eclipsed on a 94.2 d period by a tight binary composed of two K/M dwarfs (Ab1 and Ab2) that also eclipse each other; an eccentric, eclipsing binary composed of two G stars (Ba and Bb); and another faint eclipsing binary composed of two stars of unknown spectral type (Ca and Cb). In addition to its many eclipses, the system is an triple-lined spectroscopic multiple (Aa, Ba, and Bb) and the primary (Aa) is a hybrid pulsator that exhibits high amplitude pressure and gravity modes (g-modes). Furthermore, its g-modes are arrayed in a period-spacing pattern, which greatly assists with mode identification and asteroseismic modelling. In aggregate, this richness in physics offers an excellent opportunity to obtain a precise physical characterisation for some of the stars in this system. Aims. In this work we estimate the stellar parameters of the primary (Aa) by performing asteroseismic analysis on its period-spacing pattern. Methods. We used the <ns0:monospace>C-3PO</ns0:monospace> neural network to perform asteroseismic modelling of the g-mode period-spacing pattern of Aa, examining the interplay of this information with external constraints from spectroscopy (Teff and log(g)) and eclipse modelling (R). To estimate the level of uncertainty due to different frequency extraction and pattern identification processes, we considered four different variations of 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 Markov chain Monte Carlo (MCMC) grid search on four different stellar grids. Results. The externally constrained model that best fits the period-spacing pattern arrives at estimates of the stellar properties for Aa of M = 1.51 ± 0.05 M⊙, Xc = 0.43 ± 0.04, R = 1.66 ± 0.1 R⊙, fov = 0.010, Ωc = 1.58 ± 0.01 d−1 with rigid rotation to within the measurement errors, log(Teff) = 3.856 ± 0.008 dex, log(g) = 4.18 ± 0.04 dex, and log(L) = 0.809 ± 0.005 dex, which agree well with previous measurements from eclipse modelling, spectroscopy, and the Gaia DR3 luminosity. Conclusions. We find that the near-core properties of the best-fitting asteroseismic models are consistent with external constraints from eclipse modelling and spectroscopy. For stellar properties not related to the near-core region, external constraints on the asteroseismic best-fitting models are informative. 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 ± 100 Myr) is considerably older than the young age (35 Myr) 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. Improved future modelling could come from detailed coverage of metallicity effects and a careful treatment of envelope physics.