KIC 4150611: A quadruply eclipsing heptuple star system with a g-mode period-spacing pattern. Eclipse modelling of the triple and spectroscopic analysis.

KIC 4150611 is a high-order multiple composed of a triple system.\ It comprises: (1) a F1V primary (Aa) that is eclipsed on a 94.2d period by a tight 1.52d binary composed of two dim K/M dwarfs (Ab1 and Ab2), which also eclipse each other; (2) an 8.65d eccentric, eclipsing binary composed of two G stars (Ba and Bb); and (3) 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 SB3 spectroscopic multiple (Aa, Ba, and Bb), and the primary (Aa) is a hybrid pulsator that exhibits high amplitude pressure and gravity modes. In aggregate, this richness in physics offers an excellent opportunity to obtain a precise physical characterisation of some of the stars in this system. In this work we aim to characterise the F1V primary by modelling its complex eclipse geometry and disentangled stellar spectra in preparation for follow-up work that will focus on its pulsations. We employed a novel photometric analysis of the complicated eclipse geometry of Aa to obtain the orbital and stellar properties of the triple. We acquired 51 TRES spectra at the Fred L. Whipple Observatory, calculating radial velocities and orbital elements of Aa (SB1) and the B binary (SB2). These spectra and radial velocities were used to perform spectral disentangling for Aa, Ba, and Bb. Spectral modelling was applied to the disentangled spectrum of Aa to obtain atmospheric properties. From our eclipse modelling we obtain precise stellar properties of the triple, including the mass ratios ($M_ Aa /(M_ Ab1 +M_ Ab2 Ab1 /M_ Ab2 the separation ratio Aab /a_ Ab1Ab2 0.01$), orbital periods Aab Ab1Ab2 and stellar radii ( R R R Via radial velocity fitting and spectral disentangling, we find orbital elements for Aa, Ba, and Bb that are in excellent agreement with each other and with previous results in the literature. Spectral modelling on the disentangled spectrum of Aa provides constraints on the effective temperature eff K), surface gravity (log$(g) = 4.14 0.18$ dex), micro-turbulent velocity micro rotation velocity ($v i = 127 and metallicity M/H