The binary star θ¹ Ori C: orbital elements, evolutionary parameters and chemical composition

About 200 echelle spectra, obtained at the 1-m and 6-m telescopes of the Special Astrophysical Observatory (SAO) of the Russian Academy of Sciences (RAS), with high spectral resolution and signal-to-noise ratio, were used to investigate the radial velocity variability with time in both components of the θ ¹  Ori C binary system during its periastron passage. The quality of our spectra have allowed us to find a methodical approach for the spectroscopic study of the orbital motions of both components and to select lines suitable for this goal. The analysis has shown that the He ii λ 4541, 5411 lines are suitable for the primary component, and the Si iii λ 4552 line is suitable for the secondary component. Radial velocities thus measured for both components from the spectra obtained over 20 yr, along with the interferometric observations of the relative positions of the components, were used to construct a combined three-dimensional orbit of the system, in order to derive its reliable orbital parameters. Orbital elements were determined with good accuracy. For the dynamical distance, we have found a value of about d = 415 ± 6 pc, and for the system mass we find $M_{\rm sys}=44.8\pm 4.5\, {\rm M}_\odot$ . We apply a special method to calculate the synthetic spectra in binaries, taking into account the contribution of both components in their radiation, for the theoretical analysis of the observable spectra of θ ¹  Ori C. Atmospheric parameters are refined for the primary, and are determined for the secondary component for the first time. The chemical composition of θ ¹  Ori C is determined, which coincides with the chemical composition of its surrounding nebula.