Investigating 39 Galactic Wolf-Rayet stars with VLTI/GRAVITY: Uncovering a long-period binary desert

Context. Wolf-Rayet stars (WRs) represent one of the final evolutionary stages of massive stars and are thought to be the immediate progenitors of stellar-mass black holes. Their multiplicity characteristics form an important anchor point in single and binary population models for predicting gravitational-wave progenitors. Recent spectroscopic campaigns have suggested incompatible multiplicity fractions and period distributions for N- and C-rich Galactic WRs (WNs and WCs) at both short and long orbital periods, in contradiction with evolutionary model predictions. Aims. In this work, we employed long-baseline infrared interferometry to investigate the multiplicity of WRs at long periods and explored the nature of their companions. We present a magnitude-limited (K < 9; V < 14) survey of 39 Galactic WRs, including 11 WN, 15 WC, and 13 H-rich WN (WNh) stars. Methods. We used the K-band instrument GRAVITY at the Very Large Telescope Interferometer (VLTI) in Chile. The sensitivity of GRAVITY at spatial scales of ∼1 to 200 milliarcseconds and flux contrast of 1% allowed an exploration of periods in the range 10²-10⁵ d and companions down to ∼5 M_Ȯ. We carried out a companion search for all our targets, with the aim of either finding wide companions or calculating detection limits. We also explored the rich GRAVITY dataset beyond a multiplicity search to look for other interesting properties of the WR sample. Results. We detected wide companions with VLTI/GRAVITY for only four stars in our sample: WR 48, WR 89, WR 93, and WR 115. Combining our results with spectroscopic studies, we arrived at observed multiplicity fractions of f_obs^WN = 0.55 ± 0.15, f_obs^WC = 0.40 ± 0.13, and f_obs^WNh = 0.23 ± 0.12. The multiplicity fractions and period distributions of WNs and WCs are consistent in our sample. For single WRs, we placed upper limits on the mass of potential companions down to ∼5 M_Ȯ for WNs and WCs, and ∼7 M_Ȯ for WNh stars. In addition, we also found other features in the GRAVITY dataset, such as (i) a diffuse extended component contributing significantly to the K-band flux in over half the WR sample; (ii) five known spectroscopic binaries resolved in differential phase data, which constitutes an alternative detection method for close binaries; and (iii) spatially resolved winds in four stars: WR 16, WR 31a, WR 78, and WR 110. Conclusions. Our survey reveals a lack of intermediate- (a few hundred days) and long- (a few years to decades) period WR systems. The 200d peak in the period distributions of WR+OB and BH+OB binaries predicted by Case B mass-transfer binary evolution models is not seen in our data. The rich companionship of their O-type progenitors in this separation range suggests that the WR progenitor stars expand and interact with their companions, most likely through unstable mass transfer, resulting in either a short-period system or a merger.