Towards a consistent model of the hot quadruple system HD 93206 = QZ Carin\ae: II. N-body model

HD 93206 is early-type massive stellar system, composed of components resolved by direct imaging (Ab, Ad, B, C, D) as well as a compact sub-system (Aa1, Aa2, Ac1, Ac2). Its geometry was already determined on the basis of extensive photometric, spectroscopic and interferometric observations. However, the fundamental absolute parameters are still not known precisely enough. We use an advanced N-body model to account for all mutual gravitational perturbations among the four close components, and all observational data types, including: astrometry, radial velocities, eclipse timing variations, squared visibilities, closure phases, triple products, normalized spectra, and spectral-energy distribution (SED). The respective model has 38 free parameters, namely three sets of orbital elements, component masses, and their basic radiative properties ($T$, $\log g$, $v_{\rm rot}$). We revised the fundamental parameters of QZ Car as follows. For a model with the nominal extinction coefficient $R_V \equiv A_V/E(B-V) = 3.1$, the best-fit masses are $m_1 = 26.1\,M_{\rm S}$, $m_2 = 32.3\,M_{\rm S}$, $m_3 = 70.3\,M_{\rm S}$, $m_4 = 8.8\,M_{\rm S}$, with uncertainties of the order of $2\,M_{\rm S}$, and the system distance $d = (2800\pm 100)\,{\rm pc}$. In an alternative model, where we increased the weights of RV and TTV observations and relaxed the SED constraints, because extinction can be anomalous with $R_V \sim 3.4$, the distance is smaller, $d = (2450\pm 100)\,{\rm pc}$. This would correspond to that of Collinder 228 cluster. Independently, this is confirmed by dereddening of the SED, which is only then consistent with the early-type classification (O9.7Ib for Aa1, O8III for Ac1). Future modelling should also account for an accretion disk around Ac2 component.Comment: A&A, submitte

Towards a consistent model of the hot quadruple system HD 93206 = QZ Carinae - I. Observations and their initial analyses

The hot nine-component system HD 93206, which contains a gravitationally bounded eclipsing Ac1+Ac2 binary ($P=5.9987$~d) and a spectroscopic Aa1+Aa2 ($P=20.734$~d) binary can provide~important insights into the origin and evolution of massive stars. Using archival and new spectra, and a~rich collection of ground-based and space photometric observations, we carried out a detailed study of this object. We provide a much improved description of both short orbits and a good estimate of the mutual period of both binaries of about 14500~d (i.e. 40 years). For the first time, we detected weak lines of the fainter component of the 6.0~d eclipsing binary in the optical region of the spectrum, measured their radial velocities, and derived a mass ratio of $M_{\rm Ac2}/M_{\rm Ac1}=1.29$, which is the opposite of what was estimated from the International Ultraviolet explorer (IUE) spectra. We confirm that the eclipsing subsystem Ac is semi-detached and is therefore in a phase of large-scale mass transfer between its components. The Roche-lobe filling and spectroscopically brighter component Ac1 is the less massive of the two and is eclipsed in the secondary minimum. We show that the bulk of the \ha emission, so far believed to be associated with the eclipsing system, moves with the primary O9.7I component Aa1 of the 20.73~d spectroscopic binary. However, the weak emission in the higher Balmer lines seems to be associated with the accretion disc around component Ac2. We demonstrate that accurate masses and other basic physical properties including the distance of this unique system can be obtained but require a more sophisticated modelling. A~first step in this direction is presented in the accompanying Paper~II (Bro\v{z} et al.).Comment: 20 pages, 12 Figure