Towards a consistent model of the hot quadruple system HD 93206 = QZ Carinæ

II. N-body model^⋆,⋆⋆

¹ Charles University, Faculty of Mathematics and Physics, Institute of Astronomy, V Holešovičkách 2, 18000 Prague, Czech Republic
e-mail: mira@sirrah.troja.mff.cuni.cz
² Department of Physics, High Point University, One University Way, High Point, NC 27268, USA
³ Dr. Karl Remeis-Observatory & ECAP, Astronomical Institute, Friedrich-Alexander-University Erlangen-Nuremberg, Sternwartstr. 7, 96049 Bamberg, Germany
⁴ Astronomisches Institut, Ruhr-Universität Bochum, Universitätsstr. 150, 44801 Bochum, Germany
⁵ Instituto de Astronomía, Universidad Católica del Norte, Avenida Angamos 0610, Antofagasta, Chile
⁶ Instituto de Astronomia, Geofísica e Ciencias Atmosféricas, Universidade de São Paulo, Rua do Matão 1226, Cidade Universitária, 05508-900 São Paulo, SP, Brazil
⁷ Auckland Observatory, PO Box 24180 Royal Oak, Auckland, New Zealand
⁸ Variable Stars South, PO Box 173 Awanui 0451, New Zealand
⁹ Variable Stars South, Congarinni Observatory, Congarinni, NSW 2447, Australia
¹⁰ Variable Stars South, and Astronomical Society of Southern Africa, Henley Observatory, Henley on Klip, Gautenburg, South Africa
¹¹ AAVSO, 106 Hawking Pond Road, Center Harbor, NH 03226, USA
¹² Mirranook Observatory, Boorolong Rd Armidale, NSW 2350, Australia
¹³ Hvar Observatory, Faculty of Geodesy, Zagreb University, Kačićeva 26, 10000 Zagreb, Croatia
¹⁴ Eukaryotic Pathogens Innovation Center, Clemson University, Clemson, South Carolina 29634, USA

Received: 21 March 2022
Accepted: 10 July 2022

Abstract

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 ≡ A_V/E(B − V) = 3.1, the best-fit masses are m₁ = 26.1 M_S, m₂ = 32.3 M_S, m₃ = 70.3 M_S, and m₄ = 8.8 M_S, with uncertainties of the order of 2 M_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 ∼ 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.