Long-term monitoring of $\mathsf{\theta^1}$ Ori C: the spectroscopic orbit and an improved rotational period

Context. The young O-type star $\theta^1$ Ori C, the brightest star of the Trapezium cluster in Orion, is one of only two known magnetic rotators among the O stars. However, not all spectroscopic variations of this star can be explained by the magnetic rotator model. We present results from a long-term monitoring to study these unexplained variations and to improve the stellar rotational period. Aims. We want to study long-term trends of the radial velocity of $\theta^1$ Ori C, to search for unusual changes, to improve the established rotational period and to check for possible period changes. Methods. We combine a large set of published spectroscopic data with new observations and analyze the spectra in a homogeneous way. We study the radial velocity from selected photo-spheric lines and determine the equivalent width of the Hα and Heii $\lambda4686$ lines. Results. We find evidence for a secular change of the radial velocity of $\theta^1$ Ori C that is consistent with the published interferometric orbit. We refine the rotational period of $\theta^1$ Ori C and discuss the possibility of detecting period changes in the near future.