The IACOB project VIII. Searching for empirical signatures of binarity in fast-rotating O-type stars

The empirical distribution of projected rotational velocities (vsini) in massive O-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 tail. We perform a complete and homogeneous search for empirical signatures of binarity in a sample of 54 fast-rotating stars with the aim of evaluating this hypothesis. This working sample has been extracted from a larger sample of 415 Galactic O-type stars which covers the full range of vsini values. 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 $\sim$18% and $\sim$70%, respectively. When comparing these percentages with those corresponding to the slow-rotating sample we find that our sample of fast rotators is characterized by a slightly larger percentage of SB1 systems ($\sim$18% vs. $\sim$13%) and a considerably smaller fraction of clearly detected SB2 systems (8% vs. 33%). Overall, there seems to be a clear deficit of spectroscopic binaries (SB1+SB2) among fast-rotating O-type stars ($\sim$26% vs. $\sim$46%). On the contrary, the fraction of runaway stars is significantly higher in the fast-rotating domain ($\sim$33-50%) than among those stars with vsini < 200 km/s. Lastly, almost 65% of the apparently single fast-rotating stars are runaways. 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.