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

Aims. HD 93206 is a massive early-type stellar system composed of components resolved by direct imaging (Ab, Ad, B, C, D) and a compact subsystem (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. Methods. 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 model has 38 free parameters, grouped into three sets of orbital elements, component masses, and their basic radiative properties (T, log g, v(rot)). Results. We revised the fundamental parameters of QZ Car as follows. For a model with the nominal extinction coefficient R-V equivalent to A(V)/E(B - V) = 3.1, the best-fit masses are m(1)=26.1M(S), m(2)=32.3M(S), m(3)=70.3M(S), and m(4)=8.8M(S), with uncertainties of the order of 2M(S), and the system distance d=(2800 +/- 100)pc. In an alternative model, where we increased the weights of the radial velocity (RV) and transit timing variation (VTT) observations and relaxed the SED constraints, because extinction can be anomalous with R-V similar to 3.4, the distance is smaller: d=(2450 +/- 100)pc. This corresponds to the distance of the Collinder 228 cluster. Independently, this is confirmed by dereddening 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 the Ac2 component.