Tracing the young massive high-eccentricity binary system $\theta^{\mathsf 1}$Orionis C through periastron passage

Context. The nearby high-mass star binary system $\theta^1$Ori C is the brightest and most massive of the Trapezium OB stars at the core of the Orion Nebula Cluster, and it represents a perfect laboratory to determine the fundamental parameters of young hot stars and to constrain the distance of the Orion Trapezium Cluster. Aims. By tracing the orbital motion of the $\theta^1$Ori C components, we aim to refine the dynamical orbit of this important binary system. Methods. Between January 2007 and March 2008, we observed $\theta^1$Ori C with VLTI/AMBER near-infrared (H- and K-band) long-baseline interferometry, as well as with bispectrum speckle interferometry with the ESO 3.6 m and the BTA 6 m telescopes (B'- and V'-band). Combining AMBER data taken with three different 3-telescope array configurations, we reconstructed the first VLTI/AMBER closure-phase aperture synthesis image, showing the $\theta^1$Ori C system with a resolution of ∼2 mas. To extract the astrometric data from our spectrally dispersed AMBER data, we employed a new algorithm, which fits the wavelength-differential visibility and closure phase modulations along the H- and K-band and is insensitive to calibration errors induced, for instance, by changing atmospheric conditions. Results. Our new astrometric measurements show that the companion has nearly completed one orbital revolution since its discovery in 1997. The derived orbital elements imply a short-period (P ≈ 11.3 yr) and high-eccentricity orbit (e ≈ 0.6) with periastron passage around 2002.6. The new orbit is consistent with recently published radial velocity measurements, from which we can also derive the first direct constraints on the mass ratio of the binary components. We employ various methods to derive the system mass (Msystem = 44 ± 7 $M_{\odot}$) and the dynamical distance (d = 410 ± 20 pc), which is in remarkably good agreement with recently published trigonometric parallax measurements obtained with radio interferometry.