Rotation is thought to be a major factor in the evolution of massive stars, especially at low metallicity, with consequences for their chemical yields, ionizing flux and final fate. Determining the natal rotation-rate distribution of stars is of high priority given its importance as a constraint on theories of massive star formation and as input for models of stellar populations in the local Universe and at high redshift. Recently, it has become clear that the majority of massive stars interact with a binary companion before they die. We investigate how this affects the distribution of rotation rates. For this purpose, we simulate a massive binary-star population typical for our Galaxy assuming continuous star formation. We find that, because of binary interaction, 20^+5_-10% of all massive main-sequence stars have projected rotational velocities in excess of 200km/s. We evaluate the effect of uncertain input distributions and physical processes and conclude that the main uncertainties are the mass transfer efficiency and the possible effect of magnetic braking, especially if magnetic fields are generated or amplified during mass accretion and stellar mergers. The fraction of rapid rotators we derive is similar to that observed. If indeed mass transfer and mergers are the main cause for rapid rotation in massive stars, little room remains for rapidly rotating stars that are born single. This implies that spin down during star formation is even more efficient than previously thought. In addition, this raises questions about the interpretation of the surface abundances of rapidly rotating stars as evidence for rotational mixing. Furthermore, our results allow for the possibility that all early-type Be stars result from binary interactions and suggest that evidence for rotation in explosions, such as long gamma-ray bursts, points to a binary origin.
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