A spectroscopic multiplicity survey of Galactic Wolf-Rayet stars. I. The northern WC sequence

It is now well established that the majority of massive stars reside in multiple systems. However, the effect of multiplicity is not sufficiently understood, resulting in a plethora of uncertainties about the end stages of massive-star evolution. In order to investigate these uncertainties, it is useful to study massive stars just before their demise. Classical Wolf-Rayet stars represent the final end stages of stars at the upper-mass end. The multiplicity fraction of these stars was reported to be ${sim}0.4$ in the Galaxy but no correction for observational biases has been attempted. The aim of this study is to conduct a homogeneous radial-velocity survey of a magnitude-limited ($V$ $leq 12$) sample of Galactic Wolf-Rayet stars to derive their bias-corrected multiplicity properties. The present paper focuses on 12 northern Galactic carbon-rich (WC) Wolf-Rayet stars observable with the 1.2m Mercator telescope on the island of La Palma. We homogeneously measured relative radial velocities (RVs) for carbon-rich Wolf-Rayet stars using cross-correlation. Variations in the derived RVs were used to flag binary candidates. We investigated probable orbital configurations and provide a first correction of observational biases through Monte-Carlo simulations. Of the 12 northern Galactic WC stars in our sample, seven show peak-to-peak RV variations larger than 10 km s$^{-1}$, which we adopt as our detection threshold. This results in an observed spectroscopic multiplicity fraction of 0.58 with a binomial error of 0.14. In our campaign, we find a clear lack of short-period (P~$<~sim$100,d), indicating that a large number of Galactic WC binaries likely reside in long-period systems. Finally, our simulations show that at the 10% significance level, the intrinsic multiplicity fraction of the Galactic WC population is at least 0.72.