A spectroscopic multiplicity survey of Galactic Wolf-Rayet stars III. The northern late-type nitrogen-rich sample

Context. Massive stars are powerful cosmic engines that have a huge impact on their surroundings and host galaxies. The majority of massive stars will interact with a companion star during their evolution. The effects of this interaction on their end-of-life products are currently poorly constrained. In the phases immediately preceding core-collapse, massive stars in the Galaxy with M-i greater than or similar to 20 M-circle dot may appear as classical Wolf-Rayet (WR) stars. The multiplicity properties of the WR population are thus required to further our understanding of stellar evolution at the upper-mass end. Aims. As the final contribution of a homogeneous radial velocity (RV) survey, this work aims to constrain the multiplicity properties of northern Galactic late-type nitrogen-rich Wolf-Rayet (WNL) stars. We compare their intrinsic binary fraction and orbital period distribution to the carbon-rich (WC) and early-type nitrogen-rich (WNE) populations from previous works. Methods. We obtained high-resolution spectra of the complete magnitude-limited sample of 11 Galactic WNL stars with the Mercator telescope on the island of La Palma. We used cross-correlation with a log-likelihood framework to measure relative RVs and flagged binary candidates based on the peak-to-peak RV dispersion. By using Monte Carlo sampling and a Bayesian framework, we computed the three-dimensional likelihood and one-dimensional posteriors for the upper period cut-off (log P-max(WNL)), power-law index (pi(WNL)), and intrinsic binary fraction (f(int)(WNL)). Results. Adopting a threshold C of 50 km s(-1), we derived f(obs)(WNL) = 0.36 +/- 0.15. Our Bayesian analysis produces f(int)(WNL) = 0.42(-0.17)(+0.15), pi(WNL) = -0 .70(-1.02)(+0.73) and log P-max(WNL) = 4 .90(-3.40)(+0.09) for the parent WNL population. The combined analysis of the Galactic WN population results in f(int)(WN) = 0.52(-0.12)(+0.14), pi(WN) = 0 .99(-0.50)(+0.57)and log P-max(WN)= 4 .99(-1.11)(+0.00). The observed period distribution of Galactic WN and WC binaries from the literature is in agreement with what is found. Conclusions. The period distribution of Galactic WN binaries peaks at P similar to 1-10 d and that of the WC population at P similar to 5000 d. This shift cannot be reconciled by orbital evolution due to mass loss or mass transfer. At long periods, the evolutionary sequence O(-> LBV) -> WN -> WC seems feasible. The high frequency of short-period WN binaries compared to WC binaries suggests that they either tend to merge, or that the WN components in these binaries rarely evolve into WC stars in the Galaxy.