Abstract: The empirical distribution of projected rotational velocities (v sin 𝑖) in massive OB-type stars is characterized by a dominant slow velocity component and a tail of fast rotators. Binary interaction has been proposed to play a dominant role in the formation of this fast-rotating tail. We perform a complete and homogeneous search for empirical signatures of binarity in a statistically meaningful sample of 54 fast-rotating Galactic O-type stars with the aim of evaluating this hypothesis.  We use new and archival multi-epoch spectra in order to detect spectroscopic binary systems. We complement this information with Gaia proper motions and TESS photometric data to aid in the identification of runaway stars and eclipsing binaries, respectively. 

The identified fraction of single-lined spectroscopic binary (SB1) systems and apparently single stars among the fast-rotating sample is ~18% and ~70\%, respectively. When comparing these percentages with those corresponding to the slow-rotating sample we find that our sample of fast rotators is characterized by a slightly larger percentage of SB1 systems (~18% vs. ~13%) and a considerably smaller fraction of clearly detected SB2 systems (8% vs. 33%).  On the contrary, the fraction of runaway stars is significantly higher in the fast-rotating domain (~33-50%) than among those stars with vsini < 200 km/s. Our empirical results seem to be in good agreement with the idea that the tail of fast-rotating O-type stars (with vsini > 200 km/s) is mostly populated by post-interaction binary products. In particular, we find that the final statistics of identified spectroscopic binaries and apparently single stars are in good agreement with newly computed predictions obtained with the binary population synthesis code BPASS and previous estimations obtained by previous authors.